To generate two ordered pairs by substituting zero for x and y, we can use:
- When x = 0:
4(0) - 8y = -32
-8y = -32
y = 4
So one ordered pair is (0, 4).
- When y = 0:
4x - 8(0) = -32
4x = -32
x = -8
So another ordered pair is (-8, 0).
To find the rate of change, we can use the formula:
rate of change = (change in y) / (change in x)
Let's use the two ordered pairs we found to calculate the rate of change:
rate of change = (4 - 0) / (0 - (-8)) = 4 / 8 = 1/2
Therefore, the rate of change for the equation 4x - 8y = -32 is 1/2.