https://file.aiquickdraw.com/mathbot/file/1729637977987iing2l4s.jpg

The equation shown in the image is \( y = 3x + 1 \), which represents a linear equation in slope-intercept form \( y = mx + b \). Here, \( m = 3 \) is the slope, and \( b = 1 \) is the y-intercept (the point where the line crosses the y-axis).

### Steps to graph the equation:

1. **Plot the y-intercept**: The y-intercept is \( (0, 1) \), so the first point to plot is at \( y = 1 \) on the y-axis.
   
2. **Use the slope**: The slope \( m = 3 \) means that for every 1 unit you move to the right on the x-axis, you move 3 units up on the y-axis. Starting from \( (0, 1) \), you can plot another point by moving 1 unit to the right (to \( x = 1 \)) and 3 units up (to \( y = 4 \)), so the next point will be \( (1, 4) \).

3. **Draw the line**: After plotting these two points, you can draw a straight line through them, which represents the equation.

Let me know if you would like more details on the graphing process or any other questions!

---

Here are 5 related questions:
1. How would the graph change if the slope were negative, like in \( y = -3x + 1 \)?
2. What happens to the line if we change the y-intercept to \( b = 0 \), giving \( y = 3x \)?
3. How would you graph a vertical line, such as \( x = 2 \)?
4. What is the slope of a horizontal line, like \( y = 5 \)?
5. Can you find the x-intercept of the line \( y = 3x + 1 \)?

**Tip**: The slope of a line tells you how steep the line is. A larger slope results in a steeper line, while a smaller slope results in a flatter line!

Learn how to graph the linear equation y = 3x + 1 by plotting the y-intercept and using the slope. This problem explains key concepts such as slope-intercept form and graphing linear equations. Ideal 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