To graph the function \( f(x) = \frac{1}{2}x - 2 \), we can follow these steps:
Step 1: Identify the slope and y-intercept
The function is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope
- \( b \) is the y-intercept
From the function \( f(x) = \frac{1}{2}x - 2 \):
- The slope \( m = \frac{1}{2} \)
- The y-intercept \( b = -2 \)
This means the graph will intersect the y-axis at the point \( (0, -2) \).
Step 2: Plot the y-intercept
Start by plotting the point \( (0, -2) \) on the graph.
Step 3: Use the slope to find another point
The slope \( \frac{1}{2} \) indicates that for every 2 units you move to the right (positive x-direction), you move up 1 unit in the positive y-direction.
- Starting from \( (0, -2) \):
- Move 2 units to the right to \( (2, -2) \).
- Then move up 1 unit to get to the point \( (2, -1) \).
Step 4: Plot the second point
Plot the point \( (2, -1) \) on the graph.
Step 5: Draw the line
Draw a straight line through the points \( (0, -2) \) and \( (2, -1) \). This line will continue indefinitely in both directions since it represents the function for all real \( x \).
Summary of points
- y-intercept: \( (0, -2) \)
- Another point: \( (2, -1) \)
Final Graph
The graph is a straight line with a positive slope of \( \frac{1}{2} \) that crosses the y-axis at \( -2 \). If you need a visual representation, you can use graphing software or tools to plot the points and draw the line.