Question

find an equation in slope-intercept form for the line through (2, -8), perpendicular to -7x+4y=-46

Answer 1

Line given:
-7x + 4y = -46
4y = 7x- 46
y = 7x/4 - 46

Slope of this line is 7/4. Slope of line perpendicular to this one will be -4/7.

New line equation will be:
y = -4x/7 + b (you can find b given this line passes through (2,-8).
-8 = - 4*2/7 + b
=> b = -8 + 8/7 = -48/7

So, equation of that perpendicular line is:
y = -4x/7 - 48/7
7y = -4x - 48

Answer 2

thank you gt