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.
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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
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