consider the following equation. 2(y+x)-5(x-y)=-8 Find the equation of the line which passes through the point (-4,12) and is perpendicula to the given line. E

Question

consider the following equation. 2(y+x)-5(x-y)=-8 Find the equation of the line which passes through the point (-4,12) and is perpendicula to the given line. Express your answer in slope-intercept form.

Answer 1

2(y+x)-5(x-y)=-8 (solve for y)

2y+5y=-8+3x

y=(3/7)x-8/7 (slope is 3/7)

Now, we look for the equation of the line which is perpendicular to this one. This means that its slope should be -7/3 (perpendicularity condition k1=-1/k2) and it has the form: y=-(7/3)x+b. In addition, it passes through the point (-4, 12).

12=-(7/3)(-4)+b

b=12+28/3=64/3

y=-(7/3)x+64/3

7x+3y=64