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,

$m_1=\frac{-1}{m}=\frac{-1}{-5}=\frac{1}{5}$

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,

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

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

$y=\frac{1}{5}x-\frac{8}{5}$