Use the​ slope-intercept form to graph the equation y equals negative three sevenths x minus 2.


The slope-intercept form of a linear equation is written as:

\[
y = mx + b
\]

Where:
- \( m \) is the slope of the line.
- \( b \) is the y-intercept, the point where the line crosses the y-axis.

In your equation \( y = -\frac{3}{7}x - 2 \):
- The slope \( m = -\frac{3}{7} \).
- The y-intercept \( b = -2 \), meaning the line crosses the y-axis at \( (0, -2) \).

### Steps to graph the equation:
1. **Plot the y-intercept**: Start by plotting the point \( (0, -2) \) on the graph.
2. **Use the slope**: The slope \( -\frac{3}{7} \) means that for every 7 units you move to the right (positive x direction), you move 3 units down (since the slope is negative).
   - From the point \( (0, -2) \), move 7 units to the right to \( (7, -2) \), then move 3 units down to \( (7, -5) \). Plot this point \( (7, -5) \).
3. **Draw the line**: Connect the two points \( (0, -2) \) and \( (7, -5) \) with a straight line.

The graph of the equation will be a straight line passing through these two points, with a downward slope.

Would you like me to provide an image of this graph? Or would you like any further details?

### Relative Questions:
1. What does the slope of a line represent?
2. How do you determine the direction of the slope from its sign?
3. How would you graph an equation with a positive slope?
4. How can you convert an equation into slope-intercept form if it's not already in that format?
5. How does changing the y-intercept affect the graph?

**Tip:** When graphing, always start by plotting the y-intercept, and use the slope to find additional points.

Use the slope-intercept form to graph the equation y equals negative three sevenths x minus 2.

Learn how to graph the linear equation y = -3/7x - 2 using the slope-intercept form. This guide explains how to find the slope and y-intercept, plot points, and draw the line, suitable for students in Grades 7-9.

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