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Graphing Quantity Values With Constant Ratios

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  • 0:01 Constant Ratio
  • 1:29 Graph
  • 2:21 Points
  • 3:38 Equation
  • 5:03 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will see what the graph looks like when all your points have the same y:x or x:y ratio. You'll also learn how to write the equation of such a graph.

Constant Ratio

When you have points with a constant ratio, it means that your y:x or x:y ratio is the same for all points. To find the y:x ratio for each point, you write your y value on the left side of the colon and your x value on the right side of the colon. To find the x:y ratio for each point, you write your x value on the left and the y value on the right side of the colon. Once you have written this ratio, you simplify it as much as you can.

For example, the point (2, 1) has an x:y ratio of 2:1 and a y:x ratio of 1:2. The point (4, 2) has an x:y ratio of 4:2 or 2:1 and a y:x ratio of 2:4 or 1:2. As you can see, we simplified this ratio as much as we can, and we left it in ratio form with one number on the left and one number on the right side of the colon. When we have points with the same constant ratio, it means that when you take the x:y or y:x ratio of each of these points, you will get the same ratio for each point. For example, the points (2, 1), (4, 2), and (6, 3) all have the same x:y constant ratio of 2:1. The y:x constant ratio here is 1:2. The y:x ratio is simply the x:y ratio in reverse.

Graph

It's actually quite interesting to see what happens when you begin to graph points that all have the same constant ratio. Let's see what happens when you plot the points (2, 1), (4, 2), and (6, 3).

constant ratio

Hmm. Looks like you are getting a straight line. What if your constant ratio was a different number? Like, what if you had a y:x constant ratio of 3? Your points then are (1, 3), (2, 6), and (3, 9). Let's see what you get when you plot these. Note that now we have a y:x ratio where our y value comes first. All our ratios 3:1, 6:2, and 9:3 simplify to 3:1.

constant ratio

Hey, look at that! You get a straight line again! This tells you that when you have a series of points with a constant ratio, your graph will be a straight line. Also, if your graph is a straight line, then all your points will have the same constant ratio.

Points

If you know the constant ratio, then you can figure out your points. For example, if you have an x:y constant ratio of 5:1, you can easily figure out your first point by simply writing the x value and the y value of the ratio itself as your first point. You get (5, 1). To find other points, you can simply start multiplying both numbers by the same multiple. You can multiply (5, 1) by 2 to get (10, 2). Multiply it by 3, and you get (15, 3). All these points will have the same x:y constant ratio of 5:1. The points (10, 2) has an x:y ratio of 10:2 = 5:1. The point (15, 3) has an x:y ratio of 15:3 = 5:1. All of them simplify to 5:1.

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