The problem asks to graph the line $y = x - 7$. Here's how to interpret and plot the line step by step:

Step-by-Step Solution:

1. Identify the Equation:
   The equation $y = x - 7$ is in the slope-intercept form $y = mx + b$, where:

   • $m$ is the slope (here $m = 1$),
   • $b$ is the y-intercept (here $b = -7$).

2. Plot the y-Intercept:
   The y-intercept is $-7$, so the point $(0, -7)$ lies on the graph. Plot this point.

3. Use the Slope:
   The slope $m = 1$ means the line rises 1 unit vertically for every 1 unit it moves horizontally. Starting from $(0, -7)$:

   • Move 1 unit right and 1 unit up to get the point $(1, -6)$.
   • Repeat to get another point, $(2, -5)$.

4. Plot and Draw the Line:
   Plot these points and extend the line through them in both directions.

Let me know if you'd like me to generate a visual graph of this or if you have further questions!

5 Related Questions:

1. What does the slope $m = 1$ tell us about the steepness of the line?
2. How would the graph change if the equation were $y = 2x - 7$?
3. What are the coordinates of the x-intercept for this line?
4. How would you graph $y = x - 7$ using a table of values?
5. What does the negative $y$-intercept ($-7$) indicate about the position of the line?

Tip: When plotting a line, always label a few key points and extend the graph to cover the range of interest!