Question

Compare the -intercepts and the rates of change of the following items.

A.The y-intercepts are the same, but the rates of change are different.

B.The items have the same y-intercept and the same rate of change.

C.The items have different y-intercepts and different rates of change.

D.The rates of change are the same, but the y-intercepts are different.

Answer 1

C. The items have different y-intercepts and different rates of change

Explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.