Question

considet the line y= -5/2x + 2 find the equation of the line that is parallel to this line and passes through the point (-5, 4)find the equation of the line that is perpendicular to this line and passes through the point (-5, 4)

Answer 1

y = mx + b

slope = -5/3

the slope of the parallel line is -5/3

$\begin{gathered} 4=-\frac{5}{3}(-5)+b \\ 4=\frac{25}{3}+b \\ 4-\frac{25}{3}=\frac{25}{3}+b-\frac{25}{3} \\ -\frac{13}{3}=b \end{gathered}$

the equation of the parallel line is

$y=-\frac{5}{3}x-\frac{13}{3}$

b. the slope of the perpendicular line is 3/5

$\begin{gathered} 4=\frac{3}{5}(-5)+b \\ 4=-3+b \\ 4+3=-3+b+3 \\ 7=b \end{gathered}$

the equation perpendiculat to this line is

$y=\frac{3}{5}x+7$