To graph the line given by the equation \( y - 5 = -\frac{1}{2}(x + 2) \), we can follow these steps:
-
Convert the equation to slope-intercept form \( y = mx + b \):
Start with the given equation: \[ y - 5 = -\frac{1}{2}(x + 2) \] Distribute \( -\frac{1}{2} \): \[ y - 5 = -\frac{1}{2}x - 1 \] Add 5 to both sides: \[ y = -\frac{1}{2}x - 1 + 5 \] Simplify: \[ y = -\frac{1}{2}x + 4 \]
Now, the slope \( m = -\frac{1}{2} \) and the y-intercept \( b = 4 \).
-
Plot the y-intercept:
The y-intercept is at the point \( (0, 4) \). This is a point on the graph.
-
Use the slope to find another point:
From the y-intercept \( (0, 4) \), use the slope \( m = -\frac{1}{2} \) to find another point. The slope indicates that for every 2 units you move to the right (positive x-direction), the value of y decreases by 1 unit.
Starting from \( (0, 4) \):
- Move 2 units right to \( x = 2 \), then move down 1 unit to \( y = 3 \). This gives us the point \( (2, 3) \).
-
Plot the second point:
The second point is \( (2, 3) \).
-
Draw the line:
Now, draw a straight line through the points \( (0, 4) \) and \( (2, 3) \). Extend the line in both directions.
You can use the points \( (0, 4) \) and \( (2, 3) \) to draft the line on your graph.