Question

1. Line I passes through the point (-12,3) and is

perpendicular to the line 3x – 2y = 8. If (0, b) is
the y-intercept of line 1, what is the value of b?

Answer 1

y = m x + b equation of straight line

3 = -12 m + b using (-12, 3)

Also y = 1.5 x - 4 is perpendicular to line 1 (rearranging terms)

so m' = 1.5 and m = -1 / 1.5 by definition of perpendicular lines

3 = -12 (-1 / 1.5) + b using m in the first equation

3 = 8 + b and b equals -5

Check: 3 = -12 (-1 / 1.5) - 5 is then our first equation

using (-12, 3)

3 = 8 - 5 = 3