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Let's work through the exercises in your image. I’ll focus on a few of them step by step:

### Question 3:
**a. Find the equation of line 2 (general form)**

The equation of line 2 is given in slope-intercept form \(y = 4 - \frac{3}{2}x\), which can be rewritten as:
\[
y = -\frac{3}{2}x + 4
\]
To convert this to general form (i.e., \(Ax + By + C = 0\)):
1. Multiply both sides by 2 to eliminate the fraction:
   \[
   2y = -3x + 8
   \]
2. Rearrange the terms:
   \[
   3x + 2y - 8 = 0
   \]
Thus, the general form of the equation for line 2 is:
\[
3x + 2y - 8 = 0
\]

**b. Find the x-intercept of line 2**

To find the x-intercept, set \(y = 0\) in the equation of the line:
\[
0 = -\frac{3}{2}x + 4
\]
Solve for \(x\):
\[
\frac{3}{2}x = 4 \quad \Rightarrow \quad x = \frac{4 \times 2}{3} = \frac{8}{3}
\]
Thus, the x-intercept is \(x = \frac{8}{3}\).

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### Question 4:
**Determine whether the given points lie on the given lines**

**(a)** The point \(A(5, -2)\) and line \(y = -x + 3\):
1. Substitute \(x = 5\) into the equation:
   \[
   y = -(5) + 3 = -5 + 3 = -2
   \]
   Since the calculated \(y = -2\) matches the point's \(y\)-coordinate, point \(A\) lies on the line.

**(b)** The point \(B(-3, \frac{3}{2})\) and the line \(3x + 8y = -5\):
1. Substitute \(x = -3\) and \(y = \frac{3}{2}\) into the equation:
   \[
   3(-3) + 8\left(\frac{3}{2}\right) = -9 + 12 = 3
   \]
   Since \(3 \neq -5\), point \(B\) does not lie on the line.

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Would you like to continue solving other questions from this page? Feel free to specify any other specific question, and I can go over it in detail.

### Follow-up Questions:
1. How do we find the y-intercept of a line from its general form?
2. What are the steps to calculate the gradient from two points?
3. How do you classify a quadrilateral given its vertices?
4. What is the geometric meaning of a system of equations having no solution?
5. How can we solve simultaneous equations using substitution?

### Tip:
To quickly verify if a point lies on a line, substitute the coordinates into the line's equation. If both sides match, the point is on the line!

Find the general form of the equation of Line 2 and the x-intercept.

Learn how to find the general form and x-intercept of a line from its slope-intercept form. This example demonstrates key concepts in coordinate geometry, including slope, intercepts, and rearranging equations to general form. Ideal for students in Grades 8-10.

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