To graph the linear function $f(x) = 3x - 4$, follow these steps:

1. Identify the slope and y-intercept:

   • The equation is in slope-intercept form: $f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, the slope $m = 3$, and the y-intercept $b = -4$. This means the line crosses the y-axis at $(0, -4)$.

2. Plot the y-intercept:

   • Begin by plotting the point $(0, -4)$ on the graph.

3. Use the slope to find another point:

   • The slope of 3 means that for every 1 unit you move to the right (along the x-axis), you move 3 units up (along the y-axis).
   • From $(0, -4)$, move 1 unit to the right to $x = 1$, and 3 units up, placing you at the point $(1, -1)$.

4. Plot the second point:

   • Plot the point $(1, -1)$.

5. Draw the line:

   • Now, draw a straight line through the points $(0, -4)$ and $(1, -1)$. This is the graph of the function.

Would you like further details or any clarifications?

Here are five related questions:

1. What is the general formula for a linear function?
2. How do you determine the slope from a graph?
3. What does the slope of a line tell us about its steepness?
4. How would the graph change if the slope were negative?
5. What is the effect of changing the y-intercept on the graph?

Tip: Always check if the slope is positive or negative, as it determines the direction of the line (upwards or downwards).