Question

Find an equation for the line perpendicular to the line 4x - 9y = - 5 having the same y-intercept as - x - 4y = -2.

Answer 1

Clear y from both equations to find the slope y intercept form of the equations

`\begin{gathered} 4x-9y=-5 \\ -9y=-4x-5 \\ y=(-4x-5)/(-9) \\ y=(4)/(9)x+(5)/(9)\text{ (Eq. 1)} \\ -x-4y=-2 \\ -4y=x-2 \\ y=(x-2)/(-4) \\ y=-(x)/(4)+(1)/(2)\text{ (Eq. 2)} \end{gathered}`

Now, find the equation for the line that is perpendicular to Eq. 1 and has the same y intercept as Eq. 2

`\begin{gathered} m1\cdot m3=-1 \\ m3=-(1)/(m1) \\ m3=-(1)/((4)/(9)) \\ m3=-(9)/(4) \\ y=-(9)/(4)x+(1)/(2)\text{ (Eq. 3)} \end{gathered}`

Eq. 3 is the equation for the line