Question

Graph these equations:
y=
1
2
x+5
y=
1
2
x+8
Click to select points on the graph.

Answer 1

To graph the equations \( y = \frac{1}{2}x + 5 \) and \( y = \frac{1}{2}x + 8 \), let's analyze them:

Both equations have the same slope (\( \frac{1}{2} \)), which means they will be parallel straight lines. The difference in their equations comes from their y-intercepts: the first line intercepts the y-axis at \( 5 \) and the second one at \( 8 \).

### Steps to Graph the Equations

1. **Graph \( y = \frac{1}{2}x + 5 \)**:
- **Y-intercept**: Start at \( (0, 5) \) on the y-axis.
- **Slope**: The slope \( \frac{1}{2} \) means you move up 1 unit and right 2 units from the y-intercept.
- Points:
- Starting at \( (0, 5) \), if you move right 2 units, you go to \( (2, 6) \).
- Moving to the right again, to \( (4, 7) \).
- Or moving left: From \( (0, 5) \), go left 2 units and down 1 unit to reach \( (-2, 4) \).

2. **Graph \( y = \frac{1}{2}x + 8 \)**:
- **Y-intercept**: Start at \( (0, 8) \) on the y-axis.
- **Slope**: The slope is also \( \frac{1}{2} \).
- Points:
- Starting at \( (0, 8) \), you move right 2 units to reach \( (2, 9) \).
- Moving to the right again to \( (4, 10) \).
- Or going left: From \( (0, 8) \), go left 2 units and down 1 unit to \( (-2, 7) \).

### Coordinates for Both Lines

- For \( y = \frac{1}{2}x + 5 \):
- Points: \( (0, 5), (2, 6), (4, 7), (-2, 4) \)

- For \( y = \frac{1}{2}x + 8 \):
- Points: \( (0, 8), (2, 9), (4, 10), (-2, 7) \)

### Plotting

Now, you can plot these points on a coordinate plane:

1. Plot the points from the first equation, \( (0, 5), (2, 6), (4, 7), (-2, 4) \), and draw a line through them.
2. Plot the points from the second equation, \( (0, 8), (2, 9), (4, 10), (-2, 7) \), and draw a line through those points.

The resulting graph consists of two parallel lines, one at \( y = \frac{1}{2}x + 5 \) and the other at \( y = \frac{1}{2}x + 8 \).