Write the equation of a line perpendicular to the line y = (2/3)x - 7 and passing through the point (4,-2).?

Question

Help please!!!

Answer 1

Line will have m = - 3/2
Passes thro`(4, - 2)
y - b = m (x - a)
y + 2 = (- 3/2) (x - 4)
y + 2 = (-3/2) x + 6
y = (-3/2) x + 4

Answer 2

Perpendicular lines have negative reciprocal slopes. So a line perpendicular to a line with slope (2/3) has slope -1/(2/3) = -3/2.

That means the equation for the perpendicular line is of the form:

y = -(3/2)x + b

For the line to pass through (4,-2), plug in those values for x and y, and solve for b:

y = -(3/2)x + b
-2 = -(3/2)*4 + b
-2 = -6 + b
4 = b

So the equation is:

y = -(3/2)x + 4