To graph the equation $y = -\frac{3}{4}x - 1$, let's follow these steps:

1. Identify the y-intercept: The equation is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, $b = -1$. So, the y-intercept is at the point $(0, -1)$.

2. Plot the y-intercept: Place a point on the graph at $(0, -1)$.

3. Determine the slope: The slope $m = -\frac{3}{4}$ means that for every 4 units you move to the right, you move 3 units down (because the slope is negative).

4. Use the slope to find another point:

   • Starting from $(0, -1)$, move 4 units to the right (positive x-direction) to $(4, -1)$.
   • Then move 3 units down (negative y-direction), arriving at the point $(4, -4)$.

5. Plot the second point: Place a point on the graph at $(4, -4)$.

6. Draw the line: Connect the two points $(0, -1)$ and $(4, -4)$ with a straight line. This line represents the graph of $y = -\frac{3}{4}x - 1$.

Would you like a detailed explanation of the process or have any questions?

Here are 5 questions that build on this information:

1. How would the graph change if the slope were positive?
2. What would be the new y-intercept if the equation were $y = -\frac{3}{4}x + 2$?
3. How do we find the x-intercept for this equation?
4. How does changing the slope affect the steepness of the line?
5. How can we use another form of the equation, such as point-slope form, to plot the graph?

Tip: Always remember that the sign of the slope indicates the direction of the line: positive slopes rise, while negative slopes fall as you move from left to right.