To solve the problem, we are given the equations of the functions:

• $f(x) = x - 4$
• $g(x) = -2x - 7$

The solution to $f(x) = g(x)$ is the $x$-coordinate where the two lines intersect.

Solve Algebraically:

Set $f(x) = g(x)$:
$x - 4 = -2x - 7$
Add $2x$ to both sides:
$3x - 4 = -7$
Add 4 to both sides:
$3x = -3$
Divide by 3:
$x = -1$

Thus, the solution is $x = -1$.

Verify Graphically:

From the graph:

• The green line (representing $g(x) = -2x - 7$) and the purple line (representing $f(x) = x - 4$) intersect at $x = -1$, confirming our solution.

Final Answer:

The solution to $f(x) = g(x)$ is $x = -1$, which corresponds to Option C.

Would you like a deeper explanation or additional examples?

Related Questions:

1. How do you find the intersection point of two linear equations graphically?
2. What are the conditions for two lines to have a unique solution?
3. How can we verify the solution of a linear system algebraically?
4. What happens if two lines are parallel?
5. How does the slope of a line affect its graph?

Tip:

When solving equations graphically, always check the intersection point's $x$-coordinate to ensure accuracy!