Question

Find the equation of line b in slope intercept formLine a is perpendicular to line bLine a passes through the point (1,-4) and (9,-6)Line b passes through the point (-6,-24)

Answer 1

First, we need to find the slope of line a, using the next formula

$m=\frac{y_2-y_1}{x_2-x_1}$

where

(1,-4)=(x1,y1)

(9,-6)=(x2,y2)

we substitute the values

$m=\frac{-6+4}{9-1}=\frac{-2}{8}=-\frac{1}{4}$

The slope of a perpendicular line to line a is the inverse of the slope we found therefore the slope of line b will be

$m_b=4$

then we will use the slope-point form to find the equation of line b

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

where

(-6,-24)=(x1,y1)

$y+24=4(x+6)$

then in order to find the equation in the slope-intercept form, we need to isolate the y

$\begin{gathered} y+24=4x+24 \\ \end{gathered}$$y=4x+24-24$$y=4x$

The equation of line b is y=4x