Question: Consider the linear function $f(x)$ shown in the graph. Solve the given equation below.
$f(x) = -7$
$x =$
Enter multiple solutions as a comma-separated list.
If no solution exists, enter "DNE".
1. **State the problem:** We need to find the value(s) of $x$ such that $f(x) = -7$ for the given linear function.
2. **Analyze the graph:** The graph shows a straight line with a positive slope, crossing the y-axis near $-3$, and passing through points approximately $(3, 0)$ and $(8, 5)$.
3. **Find the equation of the line:**
The slope $m$ is given by
$$m = \frac{5 - 0}{8 - 3} = \frac{5}{5} = 1.$$
The y-intercept $b$ is approximately $-3$.
So the linear function is
$$f(x) = x - 3.$$
4. **Set the equation to $-7$ and solve for $x$:**
$$x - 3 = -7$$
Add $3$ to both sides:
$$x - 3 + 3 = -7 + 3$$
$$x = -4$$
5. **Interpretation:** The function equals $-7$ at $x = -4$.
6. **Check if multiple solutions exist:** Since this is a linear function with slope $1$, it crosses any horizontal line exactly once, so only one solution exists.
**Final answer:**
$$x = -4$$