Question

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

Answer 1

y = -1.2x - 2

Step-by-step 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:

`(y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1)`

From the question:

x1 = -5

y1 = 4

x2 = 5

y2 = -8

Therefore:

`\begin{gathered} (y-4)/(x-(-5))=(-8-4)/(5-(-5)) \\ (y-4)/(x+5)=\frac{-12_{}}{5\text{ + 5}} \\ \frac{y\text{ - 4}}{x\text{ + 5}}=\text{ }(-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:} \\ (10y)/(10)=\text{ }(-12)/(10)x\text{ - }(20)/(10) \\ y\text{ = -1.2x - 2} \end{gathered}`

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