Let's solve the problem step by step.

We are given the function:

$f(x) = -3x + 7$

a) Find $f(3)$:

We need to evaluate $f(3)$. To do that, substitute $x = 3$ into the function:

$f(3) = -3(3) + 7 = -9 + 7 = -2$

Thus, $f(3) = -2$.

b) Solve the equation $f(x) = -5$:

To solve $f(x) = -5$, we set the function equal to $-5$:

$-3x + 7 = -5$

Now, solve for $x$:

1. Subtract 7 from both sides: $-3x = -5 - 7$ $-3x = -12$

2. Divide both sides by $-3$: $x = \frac{-12}{-3} = 4$

Thus, $x = 4$ is the solution to $f(x) = -5$.

Would you like more details or have any questions?

Here are 5 related questions to practice:

1. What is $f(0)$ for the function $f(x) = -3x + 7$?
2. Solve the equation $f(x) = 0$ for $f(x) = -3x + 7$.
3. What is the slope of the line represented by the function $f(x) = -3x + 7$?
4. How would you describe the graph of $f(x) = -3x + 7$?
5. Find $f(-2)$ for the function $f(x) = -3x + 7$.

Tip: When solving linear equations, it's helpful to first isolate the term with the variable before performing any arithmetic operations.