To solve this problem, we need to find the x-coordinate of a point on a line with a given slope and y-intercept.

Problem Analysis

1. The line has a slope $m = \frac{3}{2}$.
2. The line intercepts the y-axis at $b = -2$.
3. We need to find the x-coordinate of a point on this line where the y-coordinate is 4.

Solution

Using the slope-intercept form of a line, $y = mx + b$, we can set up the equation:

$y = \frac{3}{2}x - 2$

Since we are given that $y = 4$, we substitute this value into the equation:

$4 = \frac{3}{2}x - 2$

Now, solve for $x$:

1. Add 2 to both sides to isolate the term with $x$: $4 + 2 = \frac{3}{2}x$ $6 = \frac{3}{2}x$

2. Multiply both sides by $\frac{2}{3}$ to solve for $x$: $x = 6 \times \frac{2}{3}$ $x = 4$

Answer

The x-coordinate of the point is 4.

Would you like further details or have any questions?

Related Questions:

1. What would be the x-coordinate if the y-coordinate were 6 instead of 4?
2. How would the line change if the slope were $-\frac{3}{2}$ instead of $\frac{3}{2}$?
3. What is the equation of a line parallel to this line but passing through a different y-intercept?
4. How would the y-intercept change if we changed the equation to pass through a different y-axis value?
5. How can you determine the slope from two given points on this line?

Tip: In the slope-intercept form $y = mx + b$, the slope $m$ represents how much $y$ changes for each unit change in $x$, while $b$ gives the starting point (y-intercept) on the y-axis.