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.