Question

Find the slope and equation of line through (-2,4) & (2,-4)

Answer 1

Given:

Points (-2,4) and (2,-4)

Using the given two points, find the slope of the line.

`\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(2,-4) \\ \\ m = (y_2 - y_1)/(x_2 - x_1) \\ m=(-4-4)/(2-(-2)) \\ m=(-8)/(2+2) \\ m=(-8)/(4) \\ m=-2 \end{gathered}`

Now that we have the slope, use the slope and any of the two points to solve for the equation of the line using point slope form. In this instance we will use m = -2, and (-2,4).

`\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y - 4 = -2\left(x + 2\right) \\ y-4=-2x-4 \\ y=-2x-4+4 \\ y=-2x\cancel{-4+4} \\ y=-2x \end{gathered}`

Therefore, the slope of the line is m = -2, and the equation of the line is y = -2x.