We are given the equation:

$4 - 2y = 8 - 2x$

To graph this equation, we need to first find the x-intercept and y-intercept.

Step 1: Rewrite the equation in slope-intercept form $y = mx + b$

Let's first isolate $y$:

$4 - 2y = 8 - 2x$ Subtract 4 from both sides:

$-2y = 4 - 2x$ Now divide by $-2$ to solve for $y$:

$y = -2 + x$

So the equation is now in the form:

$y = x - 2$

Step 2: Find the intercepts

y-intercept:

The y-intercept occurs where $x = 0$. Substituting $x = 0$ into the equation $y = x - 2$:

$y = 0 - 2 = -2$

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

x-intercept:

The x-intercept occurs where $y = 0$. Substituting $y = 0$ into the equation $y = x - 2$:

$0 = x - 2$ Solving for $x$:

$x = 2$

Thus, the x-intercept is $(2, 0)$.

Step 3: Plot the points

We now have the intercepts:

• x-intercept: $(2, 0)$
• y-intercept: $(0, -2)$

These two points are enough to graph the line. You can plot them on a coordinate plane and draw a straight line through them.

Step 4: Additional point (if necessary)

If you want more accuracy in plotting, pick a third point. For example, substitute $x = 1$ into the equation $y = x - 2$:

$y = 1 - 2 = -1$

So another point is $(1, -1)$.

Now, you have three points: $(2, 0)$, $(0, -2)$, and $(1, -1)$. Plotting these will give a clear graph of the line.

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Would you like more details on any part of this process? Or do you have any questions?

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Related questions:

1. How do you find the slope of a line from its equation?
2. What is the difference between an equation in standard form and slope-intercept form?
3. How can you graph an equation without using intercepts?
4. How do you check if two lines are parallel or perpendicular based on their equations?
5. What happens if an equation doesn't have an x- or y-intercept?

Tip: Always check the slope and y-intercept directly from the equation when you're graphing a line to save time.