To graph the equation $-x + 4y = 8$ using intercepts, we need to find both the x-intercept and the y-intercept.

Step 1: Find the x-intercept.

The x-intercept occurs where $y = 0$. To find it, substitute $y = 0$ into the equation and solve for $x$:

$-x + 4(0) = 8 \quad \Rightarrow \quad -x = 8 \quad \Rightarrow \quad x = -8$

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

Step 2: Find the y-intercept.

The y-intercept occurs where $x = 0$. To find it, substitute $x = 0$ into the equation and solve for $y$:

$-(0) + 4y = 8 \quad \Rightarrow \quad 4y = 8 \quad \Rightarrow \quad y = 2$

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

Now you have two points: $(-8, 0)$ and $(0, 2)$. You can plot these points on the graph and draw a straight line through them to graph the equation.

Would you like further steps or details on how to plot the line?