Question

Write an equation of the line in slope intercept form that is is perpendicular to the equation y = -5x + 1 through the point (2,-1)?

Answer 1

`y=(1)/(5)x-(7)/(5)`

Step-by-step explanation

We want to find the equation of the line that is perpendicular to the given line:

`y=-5x+1`

First, we have to find the slope of the line. The slope of a line perpendicular to a given line is the negative inverse of the slope of the line.

The slope of the given line is -5.

Therefore, the slope of the perpendicular line is:

`\begin{gathered} m=-((1)/(-5)) \\ m=(1)/(5) \end{gathered}`

To find the equation of the line, we have to apply the point-slope method:

`y-y_1=m(x-x_1)`

where (x1, y1) is the point the line passes through.

Therefore, the equation of the line is:

`\begin{gathered} y-(-1)=(1)/(5)(x-2) \\ y+1=(1)/(5)x-(2)/(5) \\ y=(1)/(5)x-(2)/(5)-1 \\ y=(1)/(5)x-(7)/(5) \end{gathered}`

That is the equation of the line.