Answer
The graph of the lines is shown below:
Work Step by Step
Point $(-2,5)$
$a)$ $m=3$
Using the point-slope form of the equation of a line, the equation of this line is:
$y-5=3(x+2)$
$y-5=3x+6$
$y=3x+6+5$
$y=3x+11$
$b)$ $m=-3$
$y-5=-3(x+2)$
$y-5=-3x-6$
$y=-3x-6+5$
$y=-3x-1$
$c)$ $m=\dfrac{1}{3}$
$y-5=\dfrac{1}{3}(x+2)$
$y-5=\dfrac{1}{3}x+\dfrac{2}{3}$
$y=\dfrac{1}{3}x+\dfrac{2}{3}+5$
$y=\dfrac{1}{3}x+\dfrac{17}{3}$
$d)$ $m=0$
$y-5=(0)(x+2)$
$y-5=0$
$y=5$
