Find equation of two different lines through the point 4 2 t

Find equation of two different lines through the point (4, -2) that are (a) Parallel to 7x + 6y = 3, in standard form. (b) Perpendicular to 7x + 6y = 3 in slope-intercept form.

Solution

Slope of given line=-a/b=-7/6

eq of line parallel. And passing through (4,-2)is

Y-(-2)=-7/6(x-4)

7x+6y=16

Eq of line perpendicular and passing through (4,-2)

Y-(-2)=6/7(x-4)

6x-7y=38