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This lesson covers how to identify, name and label points and lines.

Welcome to Your Tutor Online video lessons. Today we will learn how to identify, name and label points and lines.

A point does not take up any space, but so that we can see it we draw a dot. Points are labeled with capital letters. You call a point by its letter, and is read “point A.”

Two points make up a line, and a line extends forever in both directions. We can represent that by drawing arrows on either side. To name a line pick any two points that are on the line. Here we have points A and B. Lines are also labeled with capital letters, so this is called “line AB.” It can be any letters on the line at all. If we had another point here, C, it can be “line AC”, “line CA”, “line CB”, all those are fine labels for this line. The symbol for a line is the two capital letters with a line over top, just remember to draw the arrows. We read this “line AB.” You can also label a line with a lower case letter. For example we can say this is “line n.”

Points can be collinear or non-collinear. Collinear just means that the points are all on the same line. A,B, and C are all collinear points. Points D, E, and F are non-collinear because you cannot draw a line that will connect all the points.

A line segment is part of line, has end points, and does not go on forever. Line segments can be measured. You name a line segment by its end points. For example here we have line segment AB. The symbol for a segment is the capital letters of the two end points with a bar on top. The order here doesn’t matter. Segment AB is the same as segment BA.

Because line segments can be measured they can be compared with one another. If two lines segments are the same lenght they are called congruent. The symbol for congruent is an equal sign with a funny hat on top. An up and down dash can also represent congruency. Segment AB is congruent to segment BC. When this happens we know that B is the midpoint of segment AC because it divides that segment into two equal parts.

When we are comparing things, such as line segments, we use the word congruent. When we are comparing measurements we use the word equal. The measurement of segment AB is equal to the measurement of segment BC.

A ray has an endpoint and extends forever in one direction. To name a ray always start with the end point and then pick one other point on the ray. This example can be called ray AH. The symbol for a ray is going to be the capital letters of the end point (first) and then any other point with a tiny ray above it. The ray above it will always point to the right regardless of the way the ray actually points.

I hope you found this lesson useful. If you have any questions leave a comment on the blog at www.YourTutorOnline.com If you have any lessons suggestions send an email to podcast[at]yourtutoronline.com Thanks for watching, class dismissed.

How to graph a linear inequality. When to use a dotted, or solid line, and which side to shade on.

Welcome to Your Tutor Online video lessons. Today will we learn how to graph linear inequalities. A linear inequality is an equation for a line. That means it will have two variables and it has a less than, greater than, less than or equal to, or great than or equal to sign instead of the equals sign. Here we have an example 2x minus 3y is less than 6.

For the most part we are just going to pretend that this less than sign is an equal sign to solve the equation into slope intercept form. The only exception is if we multiple or divide by a negative number. When that happens, flip the sign so that it points in the other direction.

To understand why we need to flip the sign lets look at this very simply example. 3 is less than 5 which is true. Now lets multiply everything by negative 1. In a normal equation this would be fine, as long as you do something to one side that you do to the other you should maintain the equation. But here we’ll get negative 3 is less than negative 5 which is not true. Negative 5 is less than negative 3. So to account for that, instead we are going to flip the sign whenever we multiply or divide by a negative. Negative 3 is greater than negative 5, which is true.

Now let’s go back to our example and put it into slope intercept form. We are going to subtract 2x from both sides. That leaves us with negative 3y is less than negative 2x plus 6. Now we divide by negative 3 and we are left with y on this side. We need to flip our sign since we are dividing by a negative number. So now it’s greater than. Negative 2 divided by negative 3 is positve two-thirds-x and 6 divided by negative 3 is negative 2.

Now that the equation is in slope intercept form, graph it as you normally would. I’m going to start at the y axis, negative 2 for the intercept, is here. Now we are going to follow our slope - up two, over three. We are going to do that one more time: up two over three. Now, before we connect the dots we need to go back and look at the equation. Graphing here is slightly different than a normal line. If the inequality has a less than or greater than sign, we will use the dashed line. If it is less than or eqaul to, or greater than or equal to we will use a solid line. If “equal” is in the name of the symbol then use a normal line. For our example, it’s greater than so we use the dashed line. We are going to use a dashed line because the points on this line are not included in the equation.

There’s one extra thing we need to do when graphing inequalities. We have to shade on one side of the line. To figure out which one, pick any point that is not on the line. I always use the point zero, zero when I can because it is the easiest to work with. Remember that in ordered pairs the first number is x and the second number is y. We are going to take those two numbers and plug them into our inequality.

Zero is greater than zero times two-thirds x is zero; negative two. Zero is greater than negative two. If that statement is true then we will shade on the side of the line that contains the point we tested for. If its false then we will just shade on the opposite side.

So, zero is greater than negative two is true, so we shade on this side of the dotted line. And thats all there is to graphing inequalities.

I hope you found this lesson useful. If you have any questions leave a comment on the blog at www.YourTutorOnline.com If you have any lessons suggestions send an email to podcast[at]yourtutoronline.com Thanks for watching, class dismissed.

I am changing my blog software from Blogger to Wordpress. A few things may look slightly different for the time being, but all of the current videos have been successfully imported, so you should be able to find what you are looking for.

Everything should be looking back to normal by weeks end (I hope). Thanks for your patience.

I am now officially on summer vacation. But, that doesn’t mean that I am not hard at work. I will be developing new lessons which will be released this fall.

If you have a topic or lesson you would like to see please let me know. I want to create lessons that people want and need.

Update: (Lessons already produced for the fall)

• Graphing Inequalities
• Points and Lines
• Solve Equations with Absolute Value
• Simplify Radicals

What would you like to see? Click on the “comments” link below to leave your feedback!

This video explains how to solve problems involving percentage. We look at a key for how to translate a percentage question into a math equation. Three examples are given.

This lesson shows the basics of adding, subtracting, multiplying and dividing decimals. An example of each type is given.

This lesson tells the basics about circles. I define what a circle is, radius, diameter, circumference and area.

Welcome to Your Tutor Online Video Podcast. In today’s lesson, we will learn some basics about circles including diameter, radius, circumference and area.

A circle has a center point. The actual circle has all the points that are the same distance away from that point. Imagine a string with one end attached to the point and a pencil at the other. If you pull the string tight and rotate it around the point we just drew, we will get a circle. This is how projector works.

The line we just drew is called a radius. I am going to use the letter R to represent it. The radius is the distance from the center to the edge of a circle. A line that passes through the circle from edge to edge and passes through the center is called the diameter. It is going to be represented by the letter D. Diameter is equal to two times the radius.

And pi. Pi is a special irrational number. This means we cannot read it as a fraction. It is used to help us find the measurements of circles. To get a little more technical, pi is the ratio of the circumference to the diameter of a circle. If you need a number close to pi, if your teacher wants you to give your answer in decimals or fraction. If you use 3.14 or 22 over 7, these two numbers are not exactly pi but they are close enough to get an idea of what the answer should be.

Now for some formulas. Circumference is a measure around the circle. It is a very similar to perimeter with polygons. Circumference is equal to pi times diameter. Area is a measurement of the region that the circle takes up. Area is equal to Pi R squared. The answer here will be units squared.

When it comes to solving problems with circles, you may be given circumference for us to find the radius or you might know the radius and we have to find the circumference. Either way you plug in what you note, the formulas that I had showed you and then solve for what you do not know and you have your answer.

We are just going to look at two examples for this lesson. Example 1, what is the circumference of a circle which has radius of 4 centimeters. From the formulas I gave you, we know this, circumference is equal to pi times diameter but we were given the radius. There is no problem. We know that diameter is equal to two times the radius or in this case, diameter is equal to 8 centimeters. We are going to take that number and plug it into our formula, and so we know circumference is equal to 8 pi centimeters.

When we have pi as per different answer, we want to rate the number first followed by pi. If your teacher wants you to give the answer as a decimal or fraction we will do 8 times 3.14 for decimals or 8 times 22 over 7 for fractions.

One more example, what is the radius of a circle whose area is 25 pi. Our formula for area is pi times r square. I am going to fill in what we do know. Area is 25 pi. We are looking for radius now. When to buy both sides by pi and they just both cancelled out, so now we have 25 is equal to r square. We can square root both sides. The square root of 25 is 5. We are going to do nor negative because we cannot have negative link for radius, so five is equal to the radius. That is the final answer.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com. If you need more help with this or other topics visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our podcast and itunes to get the latest videos.

I will see you next time. Thanks for watching. Class dismissed.

This video shows how to convert one unit of measure to another using a chart.

Welcome to Your Tutor Online Video Podcast. In today’s lesson, I will teach you how to convert any unit of measure to any number, as long as you know the conversion ratio.

I will speak for myself here and say, “I have a hard time remembering tons of different formulas in order to convert units whether to multiply or divide even if I do know the unit of measure.”

If you use the method I am about to show you, you will not be confused anymore and you will get the correct answer 100 percent of the time. Let us say we want to convert 25 centimeters to millimeters. Well, we know that there are 100 centimeters in 1 meter. We also know that there are 1000 millimeters in 1 meter.

But it is a little hard to figure out how to put those two together to go from centimeters to millimeters. No problem. First, let us set up a chart that looks something like this. It is going to have two rows and we are just going to draw one column for now. In very top left spot, we are going to put the number we want to convert 25 and also very important is we want to include the units 25 centimeters.

Now, we already know that there are 100 centimeters in 1 meter just like we said before and 1000 millimeters in 1 meter. If we go from centimeters to meters, then meters to millimeters we have our problem solved.

We are going to draw one more column for now. We are going to put our first conversion ratio into this column. To determine whether which number goes on top and which one goes on the bottom, we are going to look our original the centimeters and opposite the side is for the other centimeters that is going to go.

So centimeters are on top here, centimeters will go on the bottom down here. 100 is what the centimeters and 1 meter goes on top. We are going to repeat the process one more time to go from meters to millimeters and that goes in this last column. Meters is on top here, so we want to do the opposite to put meter on the bottom over here and 1000 millimeters goes on top.

To make sure that you set the chart up correctly, we are going to make sure that all the units cancel out except for the unit of measure we are converting to, so we are just going to treat this chart like we were multiplying fractions together. Anything in the numerator can cancel out anything in the denominator.

Centimeters is on top. Centimeters is on the bottom, so they cancel out. Meter and meter cancel out and we are left with millimeters. As long as the only unit we are left with is on top and it is not crossed out, we set up the chart correctly.

Now, it is just a simple multiplying fraction’s problem. Before you get started, you want to make sure that you cancelled out anything that you cancelled out. I see that there is 100 in the denominator and 100 in the numerator, so we will simplify that. Now, all we have is 25 times 10 is 250. Since the only unit that is not cancelled is millimeters, final answer is 250 millimeters.

I will show you just one more really use the example, how many pounds is 48 ounces? We are going to set up our chart. We are going to put 48 here, 48 ounces with the units. You might need to look it up. You can look it up in a dictionary if you need to ounces to pounds. We know you will found out that 16 ounces is equal to 1 pound.

Since we have this conversion, we are going to put 16 on the bottom so that the ounces will cancel out. We are going to pound on top. Now, we should see ounces cancelled out and this 48 divided by 16 which is equal to 3 pounds.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com. If you need more help with this or other topics visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our podcast and itunes to get the latest videos.

I will see you next time. Thanks for watching. Class dismissed.

In this lesson we will learn about the slope intercept formula. We look at what slope and intercept mean as well as how to graph the equation.

Welcome to Your Tutor Online video podcast. In this lesson we’ll learn about slope intercept form of a line.

The slope intercept form of a line helps to graph equations. The formula is y = mx + p. x and y are just going to be points in the line. m is the slope. p is the intercept. Here is an example equation for a line. y = 2x + 3. You can tell what each part of the equation is based on its position in the formula. The slope is 2, because it’s in the first spot. And the intercept is +3, because it’s in the second place.

Let’s look at slope. Slope means rise over run. Always think of it as a fraction. When slope is a whole number like in our example, it can be rewritten just with a denominator of 1. 2 over 1. The top number of the fraction is rise, and the bottom number of the fraction is run. We normally go up and to the right. If any part of the slope is negative, we’ll go on an opposite direction. So let’s start with this point. If we had a slope of 2 we go up 2 over 1, up 2 and over 1. Slope talks about how each point on the line is in relation to another.

Next let’s look at y-intercept. It’s the last number in the equation and just means where the line crosses the y-axis. For example, it’s +3, so just put a dot at positive 3 on the y-axis and that’s the line that goes up and down. And we know that this equation is some line that passes through that point. If the y-intercept is negative, we will just put the dot at the negative part on the y-axis.

Now that we know about the slope and the intercept individually, we need build up those two things together. We’re still going to use our example y = 2x + 3. To graph this we’re going to start with the y-intercept. It’s going to go on the y-axis, the up and down line at +3, (one, two, three) and put a dot.

Now we’re going to work with our slope. It’s 2. Remember that means 2 over 1, rise 2, run 1, up 2, (one, two) over 1 and put our second dot. And we’ll repeat the process one more time, (one two), and over 1. All three those points are on our line. Now I just want to connect them with a single line. And here is our line y = 2x +3.

I want to give you one more example before we finish today. And this equation involves negative numbers so you can see how to handle those on the graphing. y = -2/3x - 2. Again we’re going to start with the y-intercept at -2 and go to -2 on the y-intercept and put a dot.

This time our slope is -2/3. So we’re going to rise -2, just the same thing as going down and then run 3. So down 2, (one, two) and run 3. I’m still going to move to the right (one, two, three). Repeat the process one more time, down 2, (one, two). Run 3 (one, two, three). Three points should be enough, so I’ll connect my dots. And there’s our line.

One thing I forgot to show you in the last example is we need to add little arrows on either end of our line to show that it continues on forever.

If you have any suggestions for future lessons, e-mail us at podcast@yourtutoronline.com.

If you need more help with this or other topics, visit www.yourtutoronline.com to find a tutor or just send an e-mail to tutor@yourtutoronline.com. We provide online tutoring services in the virtual classroom you just saw on this video. Be sure to subscribe to our podcast in iTunes to get the latest videos. I’ll see you next time. Thanks for watching. Class dismissed.

This video gives formulas and examples for how to find the area of squares, rectangles, triangles, parallelograms, and trapezoids. The video also explains the difference between base and height.

Welcome to Your Tutor Online video podcast. In this lesson, we’re going to look at area for several different polygons. Area is a measurement of a region that a shape takes up. It’s measured in units squared. The easiest way to find area is just to count the number of squares that it takes up on graph paper. Look at the blue box I just drew and we can easily see the area by counting the boxes — 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. So this square has an area of 12 units squared.

Sometimes we can’t just count the squares on graph paper because it’s unavailable, so we need to learn the following formulas for area. The first and the easiest shape we’re going to look at are squares and rectangles. Squares are rectangles so they have the same area formula. Area is equal to the length times the width. Or in other words, just one side times the other side.

Here’s a very easy example. We have a rectangle with a length of 7 inches and a width of 3 inches. 7 times 3 is 21. We’re going to write the same units that we see, inches, and then we’re going to put a little 2 up above the inches to show that’s inches squared. And that way, everybody knows we’re talking about the area and not just the length.

The next shape we’re going to look at is a triangle. The formula for the area of a triangle is area is equal to one-half times the base, times the height. The base is just going to be any of the sides of the triangle, and the height extends from that base to the opposite vertex at a perpendicular angle.

Let’s look at base and height a little more closely because I know it can be confusing.
First, for a right triangle, we’re just going to pick the two legs of the right triangle for your base and height. It doesn’t matter which one because multiplication can be done in any order.

For other triangles, it gets a little more confusing. I normally just choose the side that’s closest to me to be my base, and then the height is going to go from the base to the opposite vertex, down exactly at a 90° angle.

For the flask triangle, again, I’m going to choose the side closest to me for my base. The opposite vertex is all the way over here. Drop directly down from the vertex to my base. And notice here, the height is actually outside of the triangle, which is OK.

Let’s look at an example. Now, the hardest part of figuring out the area of a triangle is to know which one is your base, and which number is your height. So we have all these numbers here, our clue is with the right angle symbol. The right angle symbol is going to join together your base and your height. So we see this side, 4 centimeters, and this side, 3 centimeters, as our base and our height. Just to refresh your memory on the area, it’s equal to one-half base times the height. 4 times 3 is 12, times one-half, is equal to 6 centimeters cubed.

Parallelograms are easy if you understand the formula for triangles. The hardest part here, again, is to figure out what the height is. But we already know our clue is that right triangle symbol. The formula for area of a parallelogram is just base times height. We’re not going to multiply by one-half this time because a parallelogram is basically two of the same triangle put together. Since it’s so similar to a triangle, we’re not going to have an example for parallelogram. You should be able to handle plugging in the numbers into the formula.

The last polygon we’re going to look at in this lesson is the trapezoid. The formula for area of a trapezoid is one-half times the quantity base 1 plus base 2, times the height. In other words, we’re going to add the two bases together first, then divided by 2, then multiply it by the height. In a trapezoid, we have one pair of parallel sides. Those two parallel sides are our bases, base 1 and base 2. Again, we have the clue, for our height, it extends between the two bases at a perpendicular angle.

Let’s look at an example. Base 1 is 9 meters, base 2 is 7 meters. We know that because these two sides are parallel with each other. The height is 4 meters because it connects the two bases at a 90° angle. So I’m going to plug that into our formula here. One-half base 1 plus base 2, times the height which is 4. 9 plus 7 is 16. 16 divided by 2 is 8. 8 times 4 is 32. You’re going to keep the same units, meters, put the little 2 on top to show that it’s meters squared.

Sometimes you’ll have polygons with extra sides that you might not know what to do with. Well, if you can break that polygon up into smaller parts of shapes that you do know how to find the area for, you’ll be able to find the area of the whole thing. Here, we have a rectangle and two triangles. Find the area of the rectangle, the area of this triangle, and the area of this triangle. Add them all together and you have the area of the whole figure.

Let’s look at an example. If we add a line to this figure, we’ll break it up into two shapes – a rectangle and a trapezoid. The area of this rectangle is 8 times 4, which is 32, and the area of the trapezoid is the base plus the base, 12 plus 8 which is 20. 20 divided by 2 is 10, times the height — 10 times 2 is 20. 32 plus 20 is 52. The units is feet squared.

If you have any suggestions for future lessons, email us at podcast@yourtutoronline.com. If you need more help with this or other topics, visit www.yourtutoronline.com to find the tutor, or just send an email to tutor@yourtutoronline.com. We provide online tutoring services in a virtual classroom you just saw on this video. Be sure to subscribe to our video podcast in iTunes to get the latest videos. I’ll see you next time. Thanks for watching. Class dismissed.