https://file.aiquickdraw.com/mathbot/file/17265590635442wvql9a0.jpg

Let's analyze the image and solve the problem step by step.

### Problem Breakdown:
1. **Given Equation for Line 2**:
   \[
   y - 4 = \frac{3}{2}(x - 1)
   \]
   This is in the form of a point-slope equation, where the slope \( m = \frac{3}{2} \) and the point \( (1, 4) \) is on the line.

2. **Part (a)**: Find, in general form, the equation of Line 2.
   - We need to express the equation in the general form \( Ax + By + C = 0 \).

3. **Part (b)**: Find the **x-intercept** of Line 2.
   - The x-intercept occurs where \( y = 0 \).

---

### Part (a): Convert to General Form

Starting from the point-slope form:
\[
y - 4 = \frac{3}{2}(x - 1)
\]
First, expand the right-hand side:
\[
y - 4 = \frac{3}{2}x - \frac{3}{2}
\]
Now, add 4 to both sides to isolate \( y \):
\[
y = \frac{3}{2}x - \frac{3}{2} + 4
\]
\[
y = \frac{3}{2}x + \frac{5}{2}
\]

To convert this to general form \( Ax + By + C = 0 \), subtract \( y \) from both sides:
\[
0 = \frac{3}{2}x - y + \frac{5}{2}
\]
Multiply the entire equation by 2 to eliminate the fractions:
\[
0 = 3x - 2y + 5
\]
Thus, the equation in general form is:
\[
3x - 2y + 5 = 0
\]

---

### Part (b): Find the x-intercept

To find the x-intercept, set \( y = 0 \) in the general form equation and solve for \( x \):
\[
3x - 2(0) + 5 = 0
\]
\[
3x + 5 = 0
\]
\[
3x = -5
\]
\[
x = -\frac{5}{3}
\]

Thus, the x-intercept is at \( x = -\frac{5}{3} \).

---

### Summary of Results:
- **Equation of Line 2 (general form)**: \( 3x - 2y + 5 = 0 \)
- **x-intercept**: \( x = -\frac{5}{3} \)

Would you like further details or have any additional questions?

---

### Related Questions:
1. How do you convert other forms of a line equation into general form?
2. What is the process for finding the y-intercept from the general form of a line equation?
3. Can you explain how to find the slope from the general form of a line equation?
4. How does the point-slope form differ from slope-intercept form?
5. What is the geometric significance of the x- and y-intercepts?

**Tip**: Always expand and simplify carefully when converting between different forms of linear equations to avoid mistakes in algebra.

Find, in general form, the equation of line 2. Hence find the x-intercept of line 2.

Discover how to find the equation of a line in general form, starting from a point-slope equation. Also, learn how to calculate the x-intercept of the line using algebraic methods. This problem is suitable for students in Grades 9-12.

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