Question

Perpendicular to the line y= 1/4x -9; passes through (1,1)

Answer 1

Let:

`m1=(1)/(4)`

The slope of the line y = 1/4x - 9

`m2`

The slope of the unknown line.

If two lines are perpendicular, it is true:

`\begin{gathered} m1\cdot m2=-1 \\ (1)/(4)\cdot m2=-1 \\ solve_{\text{ }}for_{\text{ }}m2\colon \\ m2=-4 \end{gathered}`

Let:

`(x1,y1)=(1,1)`

Using the point-slope equation:

`\begin{gathered} y-y1=m2(x-x1) \\ y-1=-4(x-1) \\ y-1=-4(x-1) \\ y-1=-4x+4 \\ y=-4x+4+1 \\ y=-4x+5 \end{gathered}`