To determine which function has the greatest rate of change (slope), let's analyze each case provided.

1. $y = 11x - 8$:

   • This is a linear function in the form $y = mx + b$, where $m = 11$.
   • Therefore, the rate of change (slope) is $11$.

2. A fitness club charges a $200 membership fee plus monthly fees of $25:

   • The total cost function can be written as $y = 25x + 200$, where $25$ is the slope (rate of change, since the fee increases by $25 per month).
   • So, the rate of change is $25$.

3. $y = -8x$:

   • This is another linear equation, where the slope $m = -8$.
   • Therefore, the rate of change is $-8$.

4. The set of points $\{(-1, -2), (1, 2), (3, 6), (5, 10), (7, 14)\}$:

   • To find the rate of change (slope), we can use the slope formula between any two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Let's take the first two points, $(-1, -2)$ and $(1, 2)$: $m = \frac{2 - (-2)}{1 - (-1)} = \frac{4}{2} = 2$ So, the rate of change is $2$.

Conclusion:

• The function with the greatest rate of change is the fitness club function with a slope of $25$.

Would you like more details on any specific part?

Here are 5 related questions to expand on this concept:

1. How does the slope affect the steepness of a line on a graph?
2. Can you explain how to calculate the slope between two points in a coordinate plane?
3. What is the significance of the y-intercept in linear equations like $y = 11x - 8$?
4. How would the slope change if the monthly fee for the fitness club increased?
5. How do you interpret a negative slope, like in $y = -8x$?

Tip: In linear equations, the larger the slope (whether positive or negative), the steeper the line will be on a graph.