The Slope Formula Lesson 2.8 Core Focus on Linear Equations

Draw a line through each pair of points. Draw a slope triangle and find the slope. 1.(1, 3) and (5, 4) 2.(−2, 6) and (1, 0) Warm-Up −2

The Slope Formula Find the slope of a line using the slope formula. Lesson 2.8

Step 1Calculate the rate of change (the change in y over the change in x) for the table above. Ginger got a job in downtown Oklahoma City. She bought a parking pass at a garage not far from her place of work. The table shows her total parking expenses based on the number of weeks she has been parking at the garage. Step 2Graph the ordered pairs on a Quadrant I coordinate plane like the one shown below. Draw a line through the points. Step 3Make a slope triangle and determine the slope of the line. Step 4What do you notice about the rate of change and the slope of the line?

Step 5If you were given the table of values in the table to the right, what would the rate of change (or slope) ratio look like? Step 6The ratio developed in Step 5 is called the “Slope Formula”. The subscripts identify two different points. Try your formula on these points from the table above: (6, 50) and (12, 86). Did you get the same slope as you did in Steps 1 and 3? Step 7You have learned three methods for finding slope: rate of change, slope triangles and the slope formula. Which method do you like the best? Why?

The Slope Formula The formula for the slope of a line that goes through a point with coordinates (x 1, y 1 ) and another point with coordinates (x 2, y 2 ) is: You read x 1 as “x sub one.” Think of it as saying “the x-coordinate of the first point.”

Use the slope formula to find the slope of each line that passes through the given points. a.(3, 2) and (8, 5) Let (3, 2) be (x 1, y 1 ) and (8, 5) be (x 2, y 2 ). Substitute the numbers into the slope formula. Example 1 Sometimes it helps to write the subscript letters over your points to stay organized: x 1 y 1 x 2 y 2 (3, 2)(8, 5)

Use the slope formula to find the slope of each line that passes through the given points. b. (1, –1) and (3, –5) Let (1, –1) be (x 1, y 1 ) and (3, –5) be (x 2, y 2 ). Substitute the numbers into the slope formula. Example 1 Continued…

Use the slope formula to find the slope of each line that passes through the given points. c. (6, –2) and (6, 4) Let (6, –2) be (x 1, y 1 ) and (6, 4) be (x 2, y 2 ). Substitute the numbers into the slope formula. Example 1 Continued… It is impossible to divide by 0 so the slope is undefined.

Remember! You have learned three methods for calculating slope. All three methods will work in any situation. Depending on the way the linear relationship is presented, there may be one method that is easier to use than the other two methods. R ATE OF C HANGE Easiest method when information is presented in an input-output table. S LOPE T RIANGLE Easiest method when information is presented in a graph. S LOPE F ORMULA Easiest method when given two ordered pairs.

You can find slope from: A table by finding rate of change. A graph using a slope triangle. The slope formula. Which way do you prefer to find slope? Why? Communication Prompt

Find the slope of each line that passes through the given points. 1.(4, 0) and (7, 9) 2.(9, 2) and (6, 4) 3.(4, −1) and (4, 3) Exit Problems 3 Undefined