Question

Write the slope-intercept form of the equation of the line with the given characteristics. Perpendicular to y = -5x + 2 and passing through (3,-1).

Answer 1

The slope intercept form of a line can be expressed as,

`y=mx+c`

Here, m is the slope of the line and c is the y intercept.

Comparing the above equation with the given equation of a line y=-5x+2, we get

m=-5.

The slope of a line perpendicular to line with slope m is -1/m.

Hence, the slope of line perpendicular to y=-5x+2 is,

`m_1=(-1)/(m)=(-1)/(-5)=(1)/(5)`

The new line is given to be passing through point with coordinates (x1, y1)=(3, -1).

The point slope form of a line passing through point with coordinates (x1, y1)=(3, -1) and having slope m1 is,

`\begin{gathered} y-y_1=m_1(x-x_1) \\ y-(-1)=(1)/(5)(x-3) \\ y+1=(1)/(5)x-(3)/(5) \\ y=(1)/(5)x-(3)/(5)-1 \\ y=(1)/(5)x-(3-5)/(5) \\ y=(1)/(5)x-(8)/(5) \end{gathered}`

Therefore, the slope-intercept form of the equation of the line perpendicular to y = -5x + 2 and passing through (3,-1) is,

`y=(1)/(5)x-(8)/(5)`