Slope = change in y/change in x. Pick any two points.
(-17 - (-5))/(-3 - 0) = -12/-3 = 4
Along the y-axis, x = 0, so the y-intercept is -5.
y = 4x - 5
Let's check.
-17 = 4(-3) - 5
-17 = -17
-5 = 4(0) - 5
-5 = -5
-1 = 4(1) - 5
-1 = -1
7 = 4(3) - 5
7 = 7
Bingo.