Question

What is an equation of the line that passes through the points (-4, 2) and (-8, -3)?

Answer 1

Answer:

$y = 1\frac{1}{4}x+7$

Step-by-step explanation:

The equation of a straight line can be written as $y=mx+b$.

With the pair of coordinates (coordinates are written in the form $(x,y)$ ) , the following can be written:

$2=-4m+b$

$-3=-8m+b$

To solve for a variable, we can use elimination:

$-4m+b-(-8m+b)=2-(-3)$  (subtract the second equation from the first)

$-4m+b+8m-b=2+3$

$4m=5$ ($b$ is eliminated)

$m=\frac{5}{4}$

$=1\frac{1}{4}$

To solve for the other variable, we can use substitution:

$2=-4m+b$

$2=-4(1\frac{1}{4})+b$

$2 = -5 + b$

$b = 7$

$\therefore y=1\frac{1}{4}x+7$ is the linear equation for the line that passes through the points $(-4, 2)$ and $(-8,-3)$