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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?

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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.

Where do the graphs of the two functions below intersect?

f(x) = 4x - 3  and  f(x) = 9x - 13

Learn how to find the intersection point of two linear functions, f(x) = 4x - 3 and f(x) = 9x - 13. Step-by-step algebraic solution to determine where the graphs meet, including solving for x and y. Ideal for Grades 7-9 students learning linear equations.

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