Let's break down and solve the problem:

We are given the following information:

• The slope of the line $m = \frac{3}{2}$
• The y-intercept (where the line crosses the y-axis) is at $y = -2$, meaning the equation of the line is in the slope-intercept form $y = mx + b$, which gives us the equation: $y = \frac{3}{2}x - 2$
• We need to find the $x$-coordinate when the $y$-coordinate is $4$.

Step 1: Plug $y = 4$ into the equation of the line

We substitute $y = 4$ into the equation: $4 = \frac{3}{2}x - 2$

Step 2: Solve for $x$

First, add 2 to both sides to get rid of the constant: $4 + 2 = \frac{3}{2}x$ $6 = \frac{3}{2}x$

Next, multiply both sides by $\frac{2}{3}$ to solve for $x$: $x = 6 \times \frac{2}{3}$ $x = 4$

Final Answer:

The $x$-coordinate is $4$.

Would you like more details or have any questions?

Related Questions:

1. How do you derive the equation of a line from two points?
2. What does the slope represent in the context of a real-world problem?
3. How do you calculate the slope if you are given two points?
4. How can you find the x-intercept of a line using its equation?
5. What is the relationship between parallel lines and their slopes?

Tip:

Always remember that the slope represents the rate of change, and for every increase of 2 units in $x$, $y$ increases by 3 units in this particular equation.