Question

Which graph represents the linear equation y equals one half times x plus 2 on the coordinate plane?

Answer 1

To graph the equation \( y = \frac{1}{2}x + 2 \), you can follow these steps:

1. **Identify the slope and y-intercept**: The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- The slope \( m \) is \( \frac{1}{2} \).
- The y-intercept \( b \) is \( 2 \), which means the graph crosses the y-axis at the point \( (0, 2) \).

2. **Find another point using the slope**: The slope \( \frac{1}{2} \) means that for every increase of \( 1 \) in \( x \), \( y \) increases by \( \frac{1}{2} \).
- Start from the y-intercept \( (0, 2) \):
- If \( x = 2 \), then \( y = \frac{1}{2}(2) + 2 = 1 + 2 = 3 \). This gives you the point \( (2, 3) \).
- If \( x = -2 \), then \( y = \frac{1}{2}(-2) + 2 = -1 + 2 = 1 \). This gives you the point \( (-2, 1) \).

3. **Plot the points**: Plot the points \( (0, 2) \) and \( (2, 3) \) on the coordinate plane.

4. **Draw the line**: Use a ruler to connect the points, extending the line in both directions. The line should have a positive slope, rising as you move from left to right.

By following these steps, you should be able to identify the correct graph that represents the linear equation \( y = \frac{1}{2}x + 2 \).