Compute the Slope of a Non-Vertical Line

Examples, videos and solutions to help Grade 8 students learn what is meant by the slope of a line.

New York State Common Core Math Grade 8, Module 4, Lesson 16

Worksheets for Grade 8

Lesson 16 Student Outcomes

• Students use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line in the coordinate plane.
  
• Students use the slope formula to compute the slope of a non-vertical line.

Lesson 16 Summary

The slope of a line can be calculated using any two points on the same line because the slope triangles formed are similar and corresponding sides will be equal in ratio. The numerator in the formula is referred to as the difference in y-values and the denominator as the difference in x-values.

Lesson 16 Classwork

Examples 1 & 2
Using what you learned in the last lesson, determine the slope of the line with the following graph:

Example 3
What is different about this line compared to the last two examples?

Exercise
Let’s investigate concretely to see if the claim that we can find slope between any two points is true.
a. Select any two points on the line to label as P and R.
b. Identify the coordinates of points P and R.
c. Find the slope of the line using as many different points as you can. Identify your points and show your work below.

Discussion
We want to show that the slope of line can be found using any two points and on the line.
Discussion
Show that the formula to calculate slope is true for horizontal lines.
Discussion
The slope of a line can be computed using any two points.

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