Question

graph the line with the equation $y = -\frac{1}{2}x + 3$.

Explanation:

Step1: Identify Slope and Y-Intercept

The equation is \( y = -\frac{1}{2}x + 3 \). In slope - intercept form \( y=mx + b \), \( m = -\frac{1}{2} \) (slope) and \( b = 3 \) (y - intercept). So, the line crosses the y - axis at \( (0,3) \).

Step2: Plot the Y - Intercept

Locate the point \( (0,3) \) on the coordinate plane (where \( x = 0 \) and \( y = 3 \)).

Step3: Use the Slope to Find Another Point

The slope \( m=-\frac{1}{2}=\frac{\text{rise}}{\text{run}} \). A negative slope means we go down 1 unit (rise) and right 2 units (run) from the y - intercept. From \( (0,3) \), moving down 1 (to \( y = 3-1 = 2 \)) and right 2 (to \( x=0 + 2=2 \)) gives the point \( (2,2) \). We can also go up 1 and left 2 (since \( -\frac{1}{2}=\frac{1}{-2} \)) from \( (0,3) \) to get \( (- 2,4) \).

Step4: Draw the Line

Connect the points (e.g., \( (0,3) \) and \( (2,2) \) or other points found using the slope) with a straight line to graph the equation.

Answer:

To graph \( y = -\frac{1}{2}x+3 \):

1. Plot the y - intercept at \( (0,3) \).
2. Use the slope \( -\frac{1}{2} \) to find another point (e.g., from \( (0,3) \), move down 1 and right 2 to get \( (2,2) \)).
3. Draw a straight line through the plotted points.