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The question asks you to graph two equations: 

1. \( y = \frac{1}{2}x + 3 \)
2. \( y = -x \)

Let's break down how to graph each.

### Graphing \( y = \frac{1}{2}x + 3 \):
- **Slope (m)**: The slope is \( \frac{1}{2} \), meaning the line rises by 1 unit for every 2 units it moves to the right.
- **Y-intercept (b)**: The y-intercept is 3, so the line crosses the y-axis at \( (0, 3) \).

Steps:
1. Start by plotting the point \( (0, 3) \).
2. From this point, apply the slope. Move 2 units to the right and 1 unit up to get another point, say \( (2, 4) \).
3. Continue using the slope to plot more points, or extend the line using a ruler.

### Graphing \( y = -x \):
- **Slope (m)**: The slope is \( -1 \), meaning the line decreases by 1 unit for every 1 unit it moves to the right.
- **Y-intercept (b)**: This line crosses the y-axis at \( (0, 0) \) because there is no constant term.

Steps:
1. Start by plotting the point \( (0, 0) \).
2. From this point, move 1 unit to the right and 1 unit down to plot points like \( (1, -1) \), \( (2, -2) \), etc.
3. Extend the line by connecting the points.

After plotting both equations, you'll see the points where the two lines intersect.

Do you need more details or have any other questions?

Here are five follow-up questions to consider:
1. How do you determine the slope of a line from its equation?
2. What is the meaning of the y-intercept in a linear equation?
3. How can you find the point where two lines intersect?
4. What would the graph of \( y = -x + 2 \) look like compared to \( y = -x \)?
5. How do changes in the slope affect the steepness of a line?

**Tip:** When graphing a line, always start by identifying the y-intercept and slope for quick plotting!

Graph y = 1/2x + 3 and y = -x on the grid below.

Learn how to graph the linear equations y = 1/2x + 3 and y = -x. This tutorial explains how to plot the lines using slope and y-intercept, following steps for Grade 8 students. Ideal for understanding graphing in slope-intercept form.

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