https://file.aiquickdraw.com/mathbot/file/17298962055136eboiypk.jpg

To graph the linear function \( f(x) = 3x - 4 \), follow these steps:

1. **Identify the slope and y-intercept:**
   - The equation is in slope-intercept form: \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, the slope \( m = 3 \), and the y-intercept \( b = -4 \). This means the line crosses the y-axis at \( (0, -4) \).

2. **Plot the y-intercept:**
   - Begin by plotting the point \( (0, -4) \) on the graph.

3. **Use the slope to find another point:**
   - The slope of 3 means that for every 1 unit you move to the right (along the x-axis), you move 3 units up (along the y-axis).
   - From \( (0, -4) \), move 1 unit to the right to \( x = 1 \), and 3 units up, placing you at the point \( (1, -1) \).

4. **Plot the second point:**
   - Plot the point \( (1, -1) \).

5. **Draw the line:**
   - Now, draw a straight line through the points \( (0, -4) \) and \( (1, -1) \). This is the graph of the function.

Would you like further details or any clarifications?

Here are five related questions:
1. What is the general formula for a linear function?
2. How do you determine the slope from a graph?
3. What does the slope of a line tell us about its steepness?
4. How would the graph change if the slope were negative?
5. What is the effect of changing the y-intercept on the graph?

**Tip:** Always check if the slope is positive or negative, as it determines the direction of the line (upwards or downwards).

Graph each linear function: f(x) = 3x - 4.

Learn how to graph the linear function f(x) = 3x - 4 step-by-step. This problem involves identifying the slope and y-intercept, plotting points, and drawing the line. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation