8th Grade Math Help: Finding the Slope on a Graph

In 8th grade, you'll spend lots of time learning about equations and how to graph them. You'll also learn techniques to interpret graphs of equations, including how to identify the slope. Keep reading to learn more!

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Identifying the Slope on a Graph

Proportional Relationships

Linear equations always represent proportional relationships between two quantities, which means that for each unit change in one variable, there will be a set amount of change in the value of the other variable. For instance, if you travel 30 miles for every one hour that you drive, this would be a proportional relationship. If you drove 25 miles the first hour and 50 miles the second, this would not be a proportional relationship, because you would not be traveling at a constant rate.

Representing Slope

A line on a graph represents the relationship between two variables, and the slope of that line tells you the unit rate at which one variable is changing relative to the other. Slope is usually represented as a fraction, because the equation for slope is (change in y)/(change in x) or 'rise over run.' The change in y is equal to the difference in the vertical positions of two points (rise), and the change in x is equal to the horizontal difference in the positions of two points (run).

How to Calculate Slope

If you're asked to calculate slope from a graph, you'll either be given two points (x, y) on the line, or you'll be given an actual graph with a line. If you're given a graph without any points labeled, you can select any two coordinate points on that line to plug into the slope equation. To find the slope from two points on a graph, follow these steps:

  1. Designate one point as 'A' and the other as 'B.' It doesn't matter which one is A and which one is B, as long as you are consistent about which is which.
  2. Subtract the value of y in Point A from the value of y in Point B. This will be the 'rise' in your slope, which is the top number.
  3. Subtract the value of x in Point A from the value of x in Point B. This number will be your slope's 'run,' and it goes on the bottom.
  4. Simplify your slope if necessary. For example, 9/6 would become 3/2.
  5. Interpret your slope. For instance, if your slope is 2/1, you could say that the y value increases by two units for every change of one unit in the value of x.
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