To graph the equation $f(x) = -\frac{3}{4}x - 6$, the first step is to identify key features of the line. Here's how you start:

1. Rewrite the equation in slope-intercept form: The equation is already in slope-intercept form, $f(x) = mx + b$, where:

   • $m = -\frac{3}{4}$ is the slope.
   • $b = -6$ is the y-intercept.

2. Plot the y-intercept:

   • The y-intercept ($b$) is the point where the line crosses the y-axis. This occurs when $x = 0$.
   • Plot the point $(0, -6)$ on the graph.

Would you like a detailed step-by-step guide for the next steps or a graph of this equation?

5 Related Questions:

1. How does the slope of a line affect its steepness and direction?
2. What are the next steps after plotting the y-intercept for graphing a linear equation?
3. How do you determine another point on the line using the slope?
4. What does it mean if the slope is negative in a linear equation?
5. Can you explain how to find the x-intercept of a line algebraically?

Tip:

When working with slopes like $-\frac{3}{4}$, remember it means "down 3 units and right 4 units" to find additional points along the line.