Solve the following system of equations graphically on the set of axes below.
y, equals, x, plus, 8
y=x+8
y, equals, minus, one quarter, x, minus, 2
y=−
4
1
x−2
To solve the system of equations graphically, we need to plot the lines for each equation on the same set of axes and find the point of intersection:
Equation 1: y = x + 8
Equation 2: y = -0.25x - 2
Now, plotting these two lines on the set of axes:
Equation 1 (y = x + 8):
- Start at y-intercept of 8, and slope is 1, so rise 1 and run 1 from the y-intercept
- Plot the first point at (0, 8) and the next point using the slope
Equation 2 (y = -0.25x - 2):
- Start at y-intercept of -2, and slope is -0.25, so rise -0.25 and run 1 from the y-intercept
- Plot the first point at (0, -2) and the next point using the slope
The point of intersection is the solution to the system of equations. The point of intersection in this case is (4, 12).