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

To answer this question, we must find the slope of line b.
 We have then:
 b = (3 - (- 2)) / (2 - (- 3))
 b = 5/5
 b = 1
 Since the lines b and c are parallel, it follows that their slopes are equal.
 Then
 mc = b = 1
 Answer:
 The slope of line c is:
 mc = 1

Answer 2

Answer:  The slope of line c is given by

$m_c=1.$

Step-by-step explanation:  Given that line b is perpendicular to line a and  line c is perpendicular to line a.

We are to find the slope of line c.

From the graph, we see that (2, 3) and (-3, -2) are two points on the line b.

We know that

the slope of a line passing through the points (p, q) and (r, s) is given by

$m=\dfrac{s-q}{r-p}.$

Therefore, the slope of line b will be

$m_b=\dfrac{-2-3}{-3-2}=\dfrac{5}{5}=1.$

Since lines a and b are perpendicular, and the product of the slopes of two perpendicular lines is -1, so we must have

 $m_b\times m_a=-1\\\\\Rightarrow 1\times m_a=-1\\\\\Rightarrow m_a=-1.$

Again, lines c and a are perpendicular, so

$m_a\times m_c=-1\\\\\Rightarrow -1\times m_c=-1\\\\\Rightarrow m_c=1.$

Therefore, the slope of line c is given by

$m_c=1.$