https://file.aiquickdraw.com/mathbot/file/1726883997288a34e83pu.jpg

The equation provided in the image is:

\[
y = \frac{1}{3}x - 4
\]

This is a linear equation in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Let's break down the components:

- **Slope (m)**: \( \frac{1}{3} \). This means for every 3 units you move horizontally to the right, the line will rise by 1 unit.
- **Y-intercept (b)**: \(-4\). This indicates that the line crosses the y-axis at the point (0, -4).

To graph this equation:

1. Start by plotting the y-intercept at (0, -4).
2. Use the slope \( \frac{1}{3} \) to find the next point. From (0, -4), move 3 units to the right (along the x-axis) and 1 unit up (along the y-axis), landing at (3, -3).
3. Plot that point, and then draw a line through the two points.

Would you like to see more detailed steps for graphing or any clarifications?

Here are five questions related to this topic for further practice:
1. How would you graph a line with a slope of \( -\frac{2}{5} \) and a y-intercept of 2?
2. What happens to the graph of a line if the slope is zero?
3. How would you identify the slope and y-intercept from the equation \( y = -2x + 1 \)?
4. How do you determine if two lines are parallel by looking at their equations?
5. What changes occur in the graph if the equation becomes \( y = \frac{1}{3}x + 2 \) instead?

**Tip:** Always plot at least two points when graphing a line, and use the slope to find additional points to ensure accuracy!

Learn how to graph the linear equation y = 1/3 x - 4 by identifying the slope and y-intercept. This tutorial is suitable for students in Grades 8-10 and covers core algebra concepts, including slope-intercept form and graphing techniques.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation