To solve this, we need to evaluate the function $f(x) = -5x + 7$ for the given values of $x$.

1. Evaluate $f(-7)$: $f(-7) = -5(-7) + 7 = 35 + 7 = 42$

2. Evaluate $f(5)$: $f(5) = -5(5) + 7 = -25 + 7 = -18$

Answers:

• $f(-7) = 42$
• $f(5) = -18$

Would you like further details on these calculations, or do you have any questions?

Here are some related questions you might find helpful:

1. How do you determine if a function is linear?
2. What are some common forms of linear functions?
3. How do changes in the slope affect the graph of a linear function?
4. How do we interpret the slope and y-intercept in a function like $f(x) = -5x + 7$?
5. How can we use function notation to evaluate functions at different points?

Tip: Remember that evaluating functions is about substituting values in place of the variable and simplifying the result!