To graph the line $y = x - 8$, let's follow these steps:

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

   • In this case, $m = 1$ and $b = -8$.
   • The slope $m = 1$ means for every 1 unit increase in $x$, $y$ increases by 1.
   • The y-intercept $b = -8$ means the line crosses the y-axis at $y = -8$.

2. Plot the y-intercept: Start by plotting the point $(0, -8)$ on the y-axis.

3. Use the slope: From the point $(0, -8)$, use the slope $m = 1$, which is a rise of 1 and a run of 1. Move 1 unit up and 1 unit to the right to get the next point $(1, -7)$. Continue this process to generate more points like $(2, -6)$, $(3, -5)$, etc.

4. Draw the line: Connect the points with a straight line, extending it through both directions.

You can now draw this line on your grid. Would you like a step-by-step graphical construction, or any further details?

Here are some additional questions for practice:

1. What would the graph look like if the equation was $y = x + 8$?
2. How would the graph change if the slope was $m = 2$ instead of $m = 1$?
3. What is the equation of a line parallel to $y = x - 8$?
4. If the equation was $y = -x - 8$, where would the line be?
5. How do you find the x-intercept of the line $y = x - 8$?

Tip: The slope tells you how steep the line is, while the y-intercept gives the starting point on the y-axis.