Question

Find the equation of the line through (-8,5) which is perpendicular to the line y = x/4 - 4

Answer 1

To find a perpendicular line using the equation of the original line, we just need to transform the slope.

The equation of the original line is:

`y=(x)/(4)-4`

So, the slope is 1/4. To get the slope of a perpendicular line, we invert it and change its sign, so the new slope is:

`s=-(1)/((1)/(4))=-4`

With the slope and a point, (-8,5), we can use the slope-intercept form for a line, which is:

`(y-y_0)=s(x-x_0)`

Where y0 and x0 are the coordinates of the point. So:

`\begin{gathered} y-5=-4(x-(-8)) \\ y=-4(x+8)+5 \\ y=-4x-32+5 \\ y=-4x-27 \end{gathered}`