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Let's walk through the problem step-by-step.

### (a) Find the value of \( m \).

The equation given is:

\[
y = \frac{1}{2}x + 2
\]

To find \( m \), we substitute \( x = -1 \) into the equation:

\[
y = \frac{1}{2}(-1) + 2 = -\frac{1}{2} + 2 = 1.5
\]

So, the value of \( m \) is **1.5**.

### (b) Plot the graph of \( y = \frac{1}{2}x + 2 \) for \( -1 \leq x \leq 2 \).

The equation \( y = \frac{1}{2}x + 2 \) is a straight line with a slope of \( \frac{1}{2} \) and a y-intercept of 2. 

Let's calculate corresponding values of \( y \) for the given range of \( x \) values:
- When \( x = -1 \), \( y = 1.5 \)
- When \( x = 0 \), \( y = 2 \)
- When \( x = 1 \), \( y = 2.5 \)
- When \( x = 2 \), \( y = 3 \)

These points are: \((-1, 1.5)\), \((0, 2)\), \((1, 2.5)\), \((2, 3)\).

### (c) Use the graph to find the value of \( y \) when \( x = 0.5 \).

Substitute \( x = 0.5 \) into the equation:

\[
y = \frac{1}{2}(0.5) + 2 = 0.25 + 2 = 2.25
\]

So, when \( x = 0.5 \), \( y = 2.25 \).

### (d) Draw the line \( y = 1.5 \) on the graph.

The line \( y = 1.5 \) is horizontal and runs parallel to the x-axis at \( y = 1.5 \). This is a straight line for all \( x \).

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Would you like help plotting the graph or further clarifications on any of these steps?

Here are 5 related questions for further practice:
1. What is the slope of the line \( y = \frac{1}{2}x + 2 \)?
2. How does the y-intercept affect the graph of a linear equation?
3. Find the value of \( y \) when \( x = -2 \) for the equation \( y = \frac{1}{2}x + 2 \).
4. Can the graph of \( y = \frac{1}{2}x + 2 \) ever cross the x-axis?
5. What happens to the graph if the slope is changed to \( \frac{1}{3} \)?

**Tip**: The slope in a linear equation indicates how steep the line is. The larger the slope, the steeper the line.

The variables x and y are connected by the equation y = (1/2)x + 2. Find the value of m for x = -1, draw the graph for -1 ≤ x ≤ 2, and find y when x = 0.5.

This problem walks through solving the linear equation y = (1/2)x + 2, finding the value of m when x = -1, plotting the graph for -1 ≤ x ≤ 2, and determining the value of y when x = 0.5. Ideal for students in Grades 7-9.

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