This is a line and there are several ways to quickly sketch a line.
you could convert to slope-intercept form y = mx + b
so y = -3/2 x + (-3/2)4 + 2 = -3/2 x -6 + 2 = -3/2 x - 4
so, the y-intercept is (0, -4) and the slope is -3/2
plot (0, -4), then go left two (run) and up three (rise)
(0 - 2, -4 + 3) = (-2, -1)
plot (-2, -1) and draw the line that contains it and (0, -4)
But since you only need two points to sketch a line, the easiest method is usually to calculate the x and y intercepts.
The x-intercept is when y = 0, so substitute 0 for y
(0) - 2 = -3/2 (x+4) = -3/2 x - 6
6 - 2 = 4 = -3/2 x
x = (-2/3) 4 = -8/3 so one point is (-8/3, 0)
the y-intercept occurs when x = 0, substitute 0 for x
y - 2 = -3/2 [(0) + 4] = -3/2 (4) = -6
y = -6 + 2 = -4 So (0,-4) is another point
plot those two points, and draw the line that contains them both.
