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Solve for a if the line through the two given points has the given slope. \left ( 4,a \right )...

Question:

Solve for {eq}a {/eq} if the line through the two given points has the given slope.

{eq}\left ( 4,a \right ) {/eq} and {eq}\left ( -2,-2a \right ), {/eq} {eq}m = -1 {/eq}

Slope of a Line:

The slope of a line is the ratio of rise over run. The slope of a line that passes through the points {eq}(x_1, y_1) {/eq} and {eq}(x_2, y_2) {/eq} is given by:

$$m= \dfrac{y_2-y_1}{x_2-x_1} $$

It is the ratio of differences of y coordinates and x coordinates.

Answer and Explanation:

The given points are:

$$(x_1,y_1)= (4, a) \\ (x_2, y_2)=(-2, -2a) $$

The slope of the line through these points is given to be: {eq}m=-1 {/eq}.

But the formula for slope is:

$$m= \dfrac{y_2-y_1}{x_2-x_1} $$

Substitute all the values here:

$$-1= \dfrac{-2a-a}{-2-4} \\ -1= \dfrac{-3a}{-6} \\ -1= \dfrac{a}{2}\\ \text{Multiplying both sides by 2}, \\ \boxed{\mathbf{a=-2}} $$


Learn more about this topic:

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How to Find and Apply The Slope of a Line

from ELM: CSU Math Study Guide

Chapter 15 / Lesson 4
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