Question

Find the equation of the line passing through the intersection of lines 3x + y -
9 = 0 and 4x + 3y - 7 = 0 and parallel to y-axis.​

Answer 1

Answer:

Lets find the point of intersection first.

x+2y = 3

4x - y = -7

solving thses two equations

x = -11/9

y = 19/9

If two lines with slopes ‘m’ and ‘n’ are perpendicular then

m*n = -1

Given line is

3x - 2y = 7

2y = 3x - 7

y = 3x/2 - 7/2

comparing with y = mx+c , where m is the slope of the line and c is the intercept

slope of the line = 3/2

Slope of the required line = -1/(3/2)

Slope of the required line = -2/3

So we have to find the equation of line passing through (-11/9, 19/9) with slope -2/3

y - y0 = m (x-x0)

y - 19/9 = (-2/3)(x- (-11/9))

EQUATION OF LINE IS

18x + 27y - 35 = 0