Relate and compare the terms slope, rate of change, y-intercept, and initial value.

Slope and rate of change of a function are similar in meaning.

Again, y -intercept and the initial value of a function are similar in meaning.

Step-by-step explanation:

The slope and the rate of change are similar in meaning.

If we consider a linear two-variable function y = mx + c ......... (1), then the slope of the function, when plotted on the graph paper, is given by m.

Again, differentiating the above equation (1) with respect to x,  

, therefore, the rate of change of y with respect to x is m.

Again, the y-intercept of the function (1) is given by c which is the distance along the y-axis from the origin at which the graph of the function intersects the y-axis.

Now, putting x = 0, from equation (1) we get, y = c. That is why the term c is called the initial value of the function.

Therefore, the y-intercept and the initial value of a function are the same. (Answer)