To find where the graphs of the two functions $f(x) = 4x - 3$ and $f(x) = 9x - 13$ intersect, we set the two functions equal to each other:

$4x - 3 = 9x - 13$

Solving for $x$:

1. Subtract $4x$ from both sides: $-3 = 5x - 13$

2. Add $13$ to both sides: $10 = 5x$

3. Divide by $5$: $x = 2$

Finding $y$-coordinate:

Substitute $x = 2$ into either equation. Using $f(x) = 4x - 3$: $f(2) = 4(2) - 3 = 8 - 3 = 5$

Intersection Point:

The graphs intersect at the point $(2, 5)$.

Would you like further details or have any questions?

Here are 5 related questions to deepen understanding:

1. How do you determine the intersection point of two quadratic functions?
2. Can two parallel lines intersect? Why or why not?
3. What is the graphical interpretation of solving $f(x) = g(x)$?
4. How do you verify an intersection point using substitution?
5. What happens if two functions have no solution when set equal?

Tip: Always check your solution by substituting it back into both equations to confirm it satisfies both.