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=-(5)/(3)(-5)+b \\ 4=(25)/(3)+b \\ 4-(25)/(3)=(25)/(3)+b-(25)/(3) \\ -(13)/(3)=b \end{gathered}`

the equation of the parallel line is

`y=-(5)/(3)x-(13)/(3)`

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

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

the equation perpendiculat to this line is

`y=(3)/(5)x+7`