Question

what does a slope of zero mean on a line graph? *
c) the line is horizontal and there is no change
d) the line is vertical
a) the line is going uphill
b) the line is going downhill

how is the rate of change related to the slope of a line? *
d) rate of change is the square of the slope
b) rate of change is the opposite of the slope
c) rate of change is unrelated to slope
a) rate of change is the same as the slope

what does the rate of change on a line graph tell you? *
c) the total distance between points on the graph
b) how fast the dependent variable changes compared to the independent variable
d) the starting value of the dependent variable
a) how fast the independent variable changes

Explanation:

1. The slope formula is $m=\frac{\Delta y}{\Delta x}$. When $m = 0$, $\Delta y=0$, meaning there is no vertical change and the line is horizontal.
2. The rate of change of a linear - function is defined as the ratio of the change in the dependent variable to the change in the independent variable, which is the same as the slope formula $m=\frac{\Delta y}{\Delta x}$.
3. The rate of change on a line graph represents how the dependent variable ($y$) changes with respect to the independent variable ($x$).

Answer:

1. C) The line is horizontal and there is no change
2. A) Rate of change is the same as the slope
3. B) How fast the dependent variable changes compared to the independent variable