https://file.aiquickdraw.com/mathbot/file/1726560189233ei9bwm8e.jpg

The question asks to:

1. **Find the general form of the equation of line 2**.
2. **Find the x-intercept of line 2**.

### Analysis of the image:

- The equation of **line 1** is given as:
  \[
  y - 4 = \frac{3}{2}(x - 1)
  \]
  This is in **point-slope form**, where the point is \( (1, 4) \) and the slope is \( \frac{3}{2} \).

- Line 2 passes through the point \( (6, 3) \) and crosses line 1 at the origin (since the diagram shows both lines meeting at \( (0,0) \)).

### Part (a) - General Form of Line 2

Since line 2 passes through the origin and \( (6, 3) \), we can calculate its slope using these two points:

\[
\text{slope of line 2} = \frac{3 - 0}{6 - 0} = \frac{1}{2}
\]

Thus, the equation of line 2 in **slope-intercept form** is:
\[
y = \frac{1}{2}x
\]

To write this in general form \( Ax + By + C = 0 \), we rearrange:
\[
\frac{1}{2}x - y = 0
\]

Multiplying the entire equation by 2 to eliminate the fraction:
\[
x - 2y = 0
\]

Thus, the general form of the equation of line 2 is:
\[
x - 2y = 0
\]

### Part (b) - X-Intercept of Line 2

To find the x-intercept of line 2, set \( y = 0 \) in the equation \( x - 2y = 0 \):

\[
x - 2(0) = 0 \quad \Rightarrow \quad x = 0
\]

Therefore, the **x-intercept** of line 2 is at the origin \( (0, 0) \).

---

Would you like more details or have any further questions?

Here are 5 related questions to explore further:

1. What is the equation of line 1 in slope-intercept form?
2. How do you find the y-intercept of a line?
3. What is the significance of point-slope form in finding equations of lines?
4. Can you verify the perpendicularity or parallelism of two lines from their slopes?
5. How do you convert a general equation of a line into slope-intercept form?

**Tip:** The x-intercept of a line is the point where \( y = 0 \), and similarly, the y-intercept is where \( x = 0 \).

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

Find the general form of a line passing through two points, including the step-by-step calculation of the slope and how to convert the equation into general form. Also, learn how to find the x-intercept using basic algebraic methods. This problem is suitable for students in Grades 8-10.

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