Graph using the slope and y-intercept.
f(x) = 
1
2
x − 1

We are given the linear function \( f(x) = \frac{1}{2}x - 1 \). To graph this, we will use the slope-intercept form of a line, which is:

\[
y = mx + b
\]

Here:
- \( m \) is the slope.
- \( b \) is the y-intercept.

### From the equation \( f(x) = \frac{1}{2}x - 1 \), we can identify:
- The **slope** \( m = \frac{1}{2} \), meaning the line rises by 1 unit for every 2 units it moves to the right.
- The **y-intercept** \( b = -1 \), meaning the line crosses the y-axis at \( (0, -1) \).

### Steps to graph the function:
1. **Plot the y-intercept**: Start at the point \( (0, -1) \) on the y-axis.
2. **Use the slope** \( \frac{1}{2} \): From \( (0, -1) \), move up 1 unit and 2 units to the right to get the second point \( (2, 0) \).
3. **Draw the line**: Connect the points and extend the line in both directions.

Would you like me to create a graph for you, or do you have any questions?

---

Here are 5 follow-up questions related to the topic:
1. What is the significance of the slope in a linear equation?
2. How does changing the slope affect the steepness of the graph?
3. What happens if the y-intercept changes but the slope remains the same?
4. How can we determine the x-intercept from this equation?
5. How would the graph look if the slope was negative?

**Tip**: Always check both the slope and y-intercept before drawing a graph to ensure accuracy.

Graph using the slope and y-intercept. f(x) = 1/2x - 1

Learn how to graph the linear equation f(x) = 1/2x - 1 by identifying the slope and y-intercept. This problem introduces key concepts like slope, y-intercept, and how to plot a line on a graph. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation