Envision Math 2.0: Grade 8, Volume 1
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Envision Math 2.0: Grade 8, Volume 1 View details
6. Connect Proportional Relationships and Slope
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Exercise 9 Page 127

Substitute the given points into the Slope Formula.

- 2

Practice makes perfect
We can calculate the slope by substituting the given points into the Slope Formula. slope = y_2-y_1/x_2-x_1 Note that it does not matter which point we choose to use for ( x_1, y_1) and ( x_2, y_2), since the result of using the Slope Formula will be the same.
slope = y_2-y_1/x_2-x_1
slope = - 5 - ( - 4.2)/2.5- 2.1
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Add and subtract terms
slope = - 5 + 4.2/2.5 - 2.1
slope = - 0.8/0.4
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Simplify
slope = - 0.8/0.4
slope = - 8/4
slope = - 2
The slope of the line that passes through the given points is - 2.

Extra

Switch Order of Points
We will confirm that it does not matter which point we choose to use for ( x_1, y_1) and ( x_2, y_2). To do so, let's change the order of points in our formula. This time we will use (2.5,-5) for (x_1,x_2), and (2.1,-4.2) for (x_1,x_2).
slope = y_2-y_1/x_2-x_1
slope=-4.2-( -5)/2.1- 2.5
â–Ľ
Simplify right-hand side
slope=-4.2+5/2.1-2.5
slope=0.8/-0.4
slope = - 0.8/0.4
slope = - 8/4
slope = - 2
Again, we got that the slope of the line that passes through the given points is -2.