Question

Find the equation of line b described below, in slope intercept form.Line a perpendicular to line bLine a passes through the points (1,-4) and (9,-6)Line b passes through the point (-6,-24)

Answer 1

First, we have to get the slope ( m ) of the Line a based on the two points given:

$m_A=\frac{y_2-y_1}{x_2-x_1}=\frac{-6-(-4)}{9-1}=\frac{-6+4}{9-1}=-\frac{2}{8}=-\frac{1}{4}$

As they are perpendicular lines, the slope of Line a is the inverse of the slope of Line b with different sign. Therefore...

$m_B=\frac{1}{-m_A}=\frac{1}{-(-\frac{1}{4})}=4$

Finally, we find the constant of the equation using the point given of Line b.

$\begin{gathered} y_B=mx+b \\ b=y_B-mx=-24-(4\cdot-6)=-24-(-24)=-24+24=0 \\ b=0 \end{gathered}$

Answer:

$\begin{gathered} y_B=mx+b=4x+0 \\ y_{}=4x \end{gathered}$