Question

If line b is perpendicular to line a, and line c is perpendicular to line a, what is the slope of line c ?

Answer 1

There are two ways you could solve this: 1) by finding the slope that is perpendicular to a (that is, the negative reciprocal) by first finding a, or 2) by finding the slope that is parallel to b (that is, the same slope) by first finding b.

Let's use the second method.

Line b passes through two points (-3, -2) and (2, 3). We find the slope through these points.

$m_b= \dfrac{y_2-y_1}{x_2-x_1}= \dfrac{3+2}{2+3}= \dfrac{5}{5}=1\\\\\\m_b=m_c\\\\\\m_c=1$