The question in the image asks to calculate the intersection point of two given linear functions:

$f(x) = -1.5x + 4 \quad \text{and} \quad g(x) = 2x - 3$

Steps to Solve:

The intersection point is where $f(x) = g(x)$. This means:

$-1.5x + 4 = 2x - 3$

Step 1: Rearrange to isolate $x$

$-1.5x - 2x = -3 - 4$ $-3.5x = -7$

Step 2: Solve for $x$

$x = \frac{-7}{-3.5} = 2$

Step 3: Solve for $y$

Substitute $x = 2$ into either equation, for example $f(x)$: $f(2) = -1.5(2) + 4 = -3 + 4 = 1$

Final Answer:

The intersection point is: $\mathbf{(2, 1)}$

Would you like further details or visualizations? Let me know if you have questions!

Related Questions:

1. How do we verify if two lines are parallel or perpendicular?
2. What happens when two lines do not intersect?
3. How can we represent this solution graphically?
4. What are some real-world applications of finding intersection points?
5. How would this process differ for nonlinear functions?

Tip:

Always double-check calculations when solving systems of equations, especially when fractions or decimals are involved.