The equation provided is $y = 3x - 7$, which is in slope-intercept form ($y = mx + b$).

Here’s how to graph the line:

1. Identify the slope ($m$) and y-intercept ($b$):

   • Slope ($m$) = $3$: This means the line rises 3 units for every 1 unit it moves to the right.
   • Y-intercept ($b$) = $-7$: This is the point where the line crosses the y-axis.

2. Plot the y-intercept ($b$):

   • Start by plotting the point $(0, -7)$ on the graph.

3. Use the slope to find another point:

   • From $(0, -7)$, apply the slope $m = 3$ (rise/run):
     • Rise 3 units up and move 1 unit to the right to get the next point at $(1, -4)$.

4. Plot the second point:

   • Mark $(1, -4)$ on the graph.

5. Draw the line:

   • Connect the two points $(0, -7)$ and $(1, -4)$ with a straight line. Extend the line in both directions and add arrows at the ends to indicate it continues indefinitely.

Let me know if you'd like me to create or verify the graph visually.

Would you like additional clarification or any questions answered?

Here are 5 follow-up questions for practice:

1. How do you determine the slope from a given line on a graph?
2. What does a negative slope signify when graphing a line?
3. How would the graph change if the slope were $\frac{1}{2}$ instead of $3$?
4. How can you convert an equation in standard form to slope-intercept form for graphing?
5. What is the importance of the y-intercept when graphing linear equations?

Tip: Always label key points on the graph (e.g., the y-intercept) for clarity.