Pearson Algebra 1 Common Core, 2011
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Pearson Algebra 1 Common Core, 2011 View details
1. Rate of Change and Slope
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Exercise 2 Page 297

Given a graph, can you think of two different ways to find the slope?

-1/5

Practice makes perfect

We are given a graph and we want to find the slope of the line. To do it, let's first recall the Slope Formula.

The Slope Formula

The slope of a line that passes through the points (x_1,y_1) and (x_2,y_2) is given by the following formula. slope = rise/run = y_2 - y_1/x_2-x_1, where x_2-x_1 ≠ 0 The x -coordinate we use first in the denominator must belong to the same ordered pair as the y -coordinate we use first in the numerator.

Observing the given graph, we can see that the line passes through the points (-2,2) and (3,1). One way to use a graph to find the slope of a line is to count the change in the x -coordinates and the change in the y-coordinates.
We can see that as the graph travels from left to right, the rise, or change in y, is -1. Similarly, the run, or change in x, is 5. slope=rise/run ⇔ m=-1/5=- 1/5 We can confirm this answer by using the other ratio from the Slope Formula. slope = y_2 - y_1/x_2-x_1 We will use the given points to find for the slope.
slope = y_2 - y_1/x_2-x_1
slope=1- 2/3-( -2)
slope=1-2/3+2
slope=-1/5
slope=-1/5
We obtained the same number as before. We can be sure the slope is - 15.