For this case we have that by definition, the slope of a line is given by:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}[/tex]
Where:
[tex](x_ {1}, y_ {1})[/tex]and [tex](x_ {2}, y_ {2})[/tex] are two points through which the line passes
According to the statement we have:
[tex]m = 3\\(x_ {1}, y_ {1}): (- 2, q)\\(x_ {2}, y_ {2}): (- 3,2)[/tex]
Substituting we have:
[tex]3 = \frac {2-q} {- 3 - (- 2)}\\3 = \frac {2-q} {- 3 + 2}\\3 = \frac {2-q} {- 1}\\-3 = 2-q\\-3-2 = -q\\-5 = -q\\q = 5[/tex]
Answer:
The value of q is 5
