Question Type 7: Finding a parallel line and perpendicular line passing through specific point for a given line Exercises

Find the equation of the line parallel to $y=-\tfrac{1}{3}x+2$ through the point $(-3,1)$.

Find the equation of the line parallel to $y = 6x - 4$ that passes through the point $(0,1)$.

Find the equation of the line perpendicular to $y = 6x - 4$ that passes through the point $(0,1)$.

A road runs along the line $y=0.5x+3$. A parallel service road must pass through $P(-4,-1)$. Find its equation.

Find the equation of the line perpendicular to $y=-\tfrac{1}{3}x+2$ through $(-3,1)$.

Given the line $3x-2y+5=0$, find the equation of the line parallel to it passing through $(4,-1)$.

Given the line $3x-2y+5=0$, find the equation of the line perpendicular to it passing through $(4,-1)$.

Given $2x+5y-7=0$, find the equation of the line perpendicular to it passing through $(2,0)$.

Find the equation of the line perpendicular to the line through $(1,2)$ and $(3,6)$ that passes through the origin.

Find the equation of the line parallel to the line through $A(1,-2)$ and $B(4,4)$ that passes through $C(-1,3)$.

A fence must be built perpendicular to the driveway given by $y=2x-5$ at the point where $x=3$. Find the equation of the fence.

Find the equation of the line perpendicular to the line through $A(1,-2)$ and $B(4,4)$ that passes through $C(-1,3)$.