Graph the line with equation \( y=0.5 x-1.5 \)

To graph the line given by the equation \( y = 0.5x - 1.5 \), we can follow these steps: 1. **Identify the slope and y-intercept**: - The equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. - Here, the slope \( m = 0.5 \) and the y-intercept \( b = -1.5 \). 2. **Plot the y-intercept**: - The y-intercept is the point where the line crosses the y-axis. This occurs at \( (0, -1.5) \). Plot this point on the graph. 3. **Use the slope to find another point**: - The slope \( 0.5 \) can be expressed as \( \frac{1}{2} \), which means that for every 2 units you move to the right (positive x-direction), you move up 1 unit (positive y-direction). - Starting from the y-intercept \( (0, -1.5) \): - Move 2 units to the right to \( (2, -1.5) \). - Move 1 unit up to \( (2, -0.5) \). Plot this point. 4. **Draw the line**: - Now that you have two points, \( (0, -1.5) \) and \( (2, -0.5) \), you can draw a straight line through these points. Extend the line in both directions. 5. **Label the graph**: - Optionally, label the line with its equation \( y = 0.5x - 1.5 \). Here is a rough sketch of the graph: ``` y | 2| * 1| * 0|------*---------------- x -1| * -2| * -3|* | | | ``` In this sketch, the points \( (0, -1.5) \) and \( (2, -0.5) \) are marked, and the line extends infinitely in both directions.