Solve the following system of equations graphically on a set of axes. y=-2x-8, y=2/3x+8

Question

On a Graph with coordinates.

Answer 1

For the first equation the y-intercept is at (0,-8). The slope is -2 (think of this as -2/1, rise over run).

Start at the point (0,-8) on your graph paper, take a run of 1 to the right, then go down 2 (rise is -2) to arrive at the point (1, -10). You can also think of the slope as 2/-1, so from (0,-8) take a run to the left one unit and then go up 2 (rise) to arrive at the point (-1, -6). Two points are sufficient, but three will help draw a straighter line. Use a straight edge.

For the 2nd equation the y-intercept is at (0, 8) with a slope of 2/3 (take a run of 3 and a rise of 2 (right and then up). You can also think of the slope as -2/-3 and take a run to the left 3 units, then go down 2).

Draw your lines accurately to determine the point where the two lines intersect. You can also keep plotting additional points on each line to arrive at the point of intersection.

The following Desmos graph shows this technique by plotting the y-intercepts as points A and B, the adding on coordinates representing rise/run to arrive at the point of intersection. After doing this on your won, visit this graph to confirm your solution.

desmos.com/calculator/swtkzk52zd