To graph the equation $8x - 4y = -32$ using the x- and y-intercepts, follow these steps:

1. Find the x-intercept:

   • Set $y = 0$ in the equation and solve for $x$. $8x - 4(0) = -32 \implies 8x = -32 \implies x = -4$ So, the x-intercept is $(-4, 0)$.

2. Find the y-intercept:

   • Set $x = 0$ in the equation and solve for $y$. $8(0) - 4y = -32 \implies -4y = -32 \implies y = 8$ So, the y-intercept is $(0, 8)$.

3. Plot the intercepts:

   • Mark the points $(-4, 0)$ and $(0, 8)$ on the graph.

4. Draw the line:

   • Connect the two intercepts with a straight line to graph the equation.

Here’s a step-by-step breakdown of the graph:

• X-intercept: $(-4, 0)$
• Y-intercept: $(0, 8)$
• Equation in slope-intercept form: $y = 2x + 8$

Would you like a visual graph of this equation? Feel free to ask any additional questions!

Relative Questions:

1. How do you determine the slope of a line using two points?
2. What happens if the line does not intersect the x-axis or y-axis?
3. How do you convert the given equation to slope-intercept form?
4. Can you explain how to find the intercepts for more complex equations?
5. How would you graph an equation if both intercepts are zero?

Tip: Always check if your line passes through the intercepts after drawing to ensure accuracy.