To graph the equation $x - 4y = 8$ using the intercepts, let's find the $x$- and $y$-intercepts and then plot the line through those points.

Step 1: Find the $x$-intercept

The $x$-intercept occurs where $y = 0$.

1. Substitute $y = 0$ into the equation: $x - 4(0) = 8$
2. Simplify to find $x$: $x = 8$

So, the $x$-intercept is at $(8, 0)$.

Step 2: Find the $y$-intercept

The $y$-intercept occurs where $x = 0$.

1. Substitute $x = 0$ into the equation: $0 - 4y = 8$
2. Solve for $y$: $-4y = 8 \Rightarrow y = -2$

So, the $y$-intercept is at $(0, -2)$.

Step 3: Plot the Intercepts and Draw the Line

On the graph:

• Plot the point $(8, 0)$ on the $x$-axis.
• Plot the point $(0, -2)$ on the $y$-axis.
• Draw a straight line passing through these two points to represent the equation $x - 4y = 8$.

Would you like additional details on how this line is derived, or any assistance with other questions?

Here are five related questions to deepen your understanding:

1. How would you rewrite the equation $x - 4y = 8$ in slope-intercept form?
2. What would the graph look like if the equation were $x + 4y = 8$?
3. How do you interpret the slope of the line from the equation $x - 4y = 8$?
4. How can you verify the intercepts algebraically?
5. What would be the effect on the intercepts if the equation were $2x - 8y = 16$?

Tip: When finding intercepts, always set the opposite variable to zero, as intercepts are the points where the line crosses each axis.