Graph the line with \( y \)-intercept 9 and slope \( -\frac{1}{2} \)

To graph the line with a \( y \)-intercept of 9 and a slope of \( -\frac{1}{2} \), we can follow these steps: 1. **Identify the \( y \)-intercept**: The \( y \)-intercept is the point where the line crosses the \( y \)-axis. Given that the \( y \)-intercept is 9, this point is \( (0, 9) \). 2. **Use the slope to find another point**: The slope of the line is \( -\frac{1}{2} \). This means that for every 2 units you move to the right (in the positive \( x \) direction), you move 1 unit down (in the negative \( y \) direction). Starting from the \( y \)-intercept \( (0, 9) \): - Move 2 units to the right: \( x = 0 + 2 = 2 \) - Move 1 unit down: \( y = 9 - 1 = 8 \) This gives us another point on the line: \( (2, 8) \). 3. **Plot the points**: Plot the points \( (0, 9) \) and \( (2, 8) \) on the graph. 4. **Draw the line**: Draw a straight line through the two points. This line represents the equation of the line with the given \( y \)-intercept and slope. The equation of the line can also be written in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. Thus, the equation of the line is: \[ y = -\frac{1}{2}x + 9 \] This line will slope downwards from left to right due to the negative slope.