Question

consider the following equation.
2x + 7 = -2y + 7
step 2 of 2 : graph the equation by plotting the x - and y - intercepts. if an intercept does not exist, or is duplicated, use another point on the line to plot the graph.
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Explanation:

Step1: Simplify the given equation

Start with $2x + 7 = -2y + 7$. Subtract 7 from both sides:
$2x = -2y$
Divide both sides by 2:
$x = -y$ or $y = -x$

Step2: Find x-intercept (y=0)

Substitute $y=0$ into $y=-x$:
$0 = -x \implies x=0$
x-intercept: $(0, 0)$

Step3: Find y-intercept (x=0)

Substitute $x=0$ into $y=-x$:
$y = -0 = 0$
y-intercept: $(0, 0)$ (duplicate of x-intercept)

Step4: Find a second point

Choose $x=2$, substitute into $y=-x$:
$y = -2$
Second point: $(2, -2)$

Answer:

Plot the points $(0, 0)$ and $(2, -2)$, then draw a straight line through them. Additional points like $(-3, 3)$ can also be used to confirm the line.