Question

What is anequation of the line that passes through the points (-5,4) and (5,–8)?

Answer 1

ANSWER

y = -1.2x - 2

EXPLANATION

We want to find the equation of the line that passes through points (-5, 4) and (5, -8).

To do this, we use the formula:

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

From the question:

x1 = -5

y1 = 4

x2 = 5

y2 = -8

Therefore:

$\begin{gathered} \frac{y-4}{x-(-5)}=\frac{-8-4}{5-(-5)} \\ \frac{y-4}{x+5}=\frac{-12_{}}{5\text{ + 5}} \\ \frac{y\text{ - 4}}{x\text{ + 5}}=\text{ }\frac{-12}{10} \\ \text{Cross multiply:} \\ 10(y\text{ - 4) = -12(x + 5)} \\ 10y\text{ - 40 = -12x -60} \\ \text{Collect like terms}\colon \\ 10y\text{ = -12x - 60 + 40} \\ 10y\text{ = -12x - 20} \\ \text{Divide through by 10:} \\ \frac{10y}{10}=\text{ }\frac{-12}{10}x\text{ - }\frac{20}{10} \\ y\text{ = -1.2x - 2} \end{gathered}$

That is the equation of the line that passes through those points.