To graph the equation $y = -\frac{3}{2}x - 1$, follow these steps:

1. Identify the slope and y-intercept:

• The equation is in slope-intercept form $y = mx + b$, where:
  • $m = -\frac{3}{2}$ (slope)
  • $b = -1$ (y-intercept)

2. Plot the y-intercept:

• Start by plotting the point $(0, -1)$ on the y-axis.

3. Use the slope to find another point:

• The slope $-\frac{3}{2}$ means "rise over run" = $-3$ units down and $2$ units to the right.
• From the point $(0, -1)$, move 3 units down and 2 units right to get the next point at $(2, -4)$.

4. Draw the line:

• Connect the points $(0, -1)$ and $(2, -4)$ with a straight line, and extend the line in both directions.

If you would like, I can generate the graph for you. Would you like the graph or further details?

Relative Questions:

1. What does the slope represent in a linear equation?
2. How would you find the x-intercept of this line?
3. What happens to the graph if you change the slope to a positive value?
4. How does changing the y-intercept affect the graph?
5. Can you explain how to graph lines when given the point-slope form?

Tip: Always check the sign of the slope to determine if the line rises or falls. A negative slope means the line falls from left to right.