Treat this problem as one involving finding the point at which two lines intersect.
One line would be y = -3x + 1; the other would be the horiz. line y = -8.
Whenever two lines intersect, the coefficients of the point of intersection satisfy both equations. Thus, we set y = y, or, in this case, -3x + 1 = -8.
Subtracting 1 from both sides, we get -3x + 1 - 1 = -8 - 1, or
-3x = -9, or (after dividing both lines by -3) x = 3.
We already know that the y-coordinate of the point of intersection / solution is y = -8, so we can write the solution as
(3, -8)
First, draw the horizontal line y = -8.
Next, draw the line y = -3x + 1. Letting x = 0, we get y = 1, which means that the y-intercept is (0,1). Place a black dot at (0,1). Now, taking info from the slope (-3), find and place a black dot at the next point, as follows:
From your dot at (0,1), move 1 unit to the right and then 3 units down. This point will be (1,-3). Place a black dot there.
Draw a line through your two black dots. You'll see that this line and the line y = -8 intersect at (3,-8).
