To find the point at which the graphs of $f(x) = 5x + 1$ and $g(x) = -2x + 15$ intersect, we need to set the two equations equal to each other and solve for $x$.

Step 1: Set $f(x)$ equal to $g(x)$

$5x + 1 = -2x + 15$

Step 2: Solve for $x$

First, add $2x$ to both sides: $5x + 2x + 1 = 15$ $7x + 1 = 15$ Next, subtract 1 from both sides: $7x = 14$ Now, divide by 7: $x = 2$

Step 3: Find $y$ by substituting $x = 2$ into either equation

Using $f(x) = 5x + 1$: $f(2) = 5(2) + 1 = 10 + 1 = 11$

So, the graphs intersect at the point $(2, 11)$.

Thus, the correct answer is $(2, 11)$.

Would you like more details or have any questions?

Here are some related questions:

1. How do you solve systems of equations graphically?
2. What does it mean when two graphs intersect?
3. How do you find the slope of a line given its equation?
4. How do you interpret the y-intercept of a linear equation?
5. Can two lines with different slopes ever be parallel?

Tip: When solving for intersection points, setting the two equations equal to each other is a key step!