To graph the equation $4x + 8 = -4y + 8$ by plotting the x- and y-intercepts, follow these steps:

Step 1: Simplify the equation

First, simplify the given equation:

$4x + 8 = -4y + 8$

Subtract 8 from both sides to cancel out the constants:

$4x = -4y$

Now, divide both sides by 4:

$x = -y$

This is the simplified equation of the line.

Step 2: Find the x-intercept

To find the x-intercept, set $y = 0$:

$x = -0 = 0$

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

Step 3: Find the y-intercept

To find the y-intercept, set $x = 0$:

$0 = -y$

So, $y = 0$.

Thus, the y-intercept is also at $(0, 0)$.

Step 4: Plot an additional point

Since the x- and y-intercepts are the same (at the origin), we need another point to graph the line. Choose any value for $x$ (or $y$) and find the corresponding $y$ (or $x$).

Let's choose $x = 1$:

$x = -y \Rightarrow 1 = -y \Rightarrow y = -1$

So, another point on the line is $(1, -1)$.

Step 5: Graph the line

Plot the points $(0, 0)$ and $(1, -1)$ on the graph, and draw a straight line through them.

Summary:

• X-intercept: $(0, 0)$
• Y-intercept: $(0, 0)$
• Additional point: $(1, -1)$

This is the graph of the equation $x = -y$, which is a straight line passing through the origin with a slope of -1.

Would you like any further explanation or a visual representation?

Related Questions:

1. How can you verify the slope of a line using its equation?
2. What happens if the x- and y-intercepts are the same point?
3. How do you determine if a line is horizontal or vertical from its equation?
4. What are the general forms of linear equations, and how do you convert between them?
5. How does changing the slope affect the graph of a line?

Tip:

When both intercepts are at the origin, choosing an additional point ensures accuracy in graphing the line.