Find the equation of the line that passes through the point of intersection of lines 2x+5y+19=0 and 4x-3y-1=0 that is perpendicular to the line 3x-2y+1=0

Question

anonymous · Answer

First of all we need to solve this system:
2x + 5y + 19= 0
4x - 3y -1 = 0

Multiply first one with -2 and some terms cancel out. We get y = -3 and if we plug in that value to one of the equations, we get x = -2. Now we have a point of intersection which is (-2 , -3 ) .

We need to rewrite 3x - 2y + 1 = 0 as  y = x3/2 + 1/2 . We can see slope of this equation is 3/2. Now we need to use $$y-y_{0} = m(x-x_{0})$$  formula to get a equation. If we plug in all values, finally we get the equation as  $$y + 3 = \frac{ 3 }{ 2 } (x + 2 )$$