Simplify the equation if possible. Then graph the equation using the $$ x $$-intercept and the $$ y $$-interce $$ 2 x-y=-2 $$

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UpStudy AI · Accepted Answer

Sure! Let's **simplify the equation** and then **graph it** using the $$ x $$-intercept and $$ y $$-intercept.

### Given Equation:
$$ 2x - y = -2 $$

### Step 1: Simplify the Equation

Let's solve for $$ y $$ to put the equation in slope-intercept form ($$ y = mx + b $$).

$$
\begin{align*}
2x - y &= -2 \
-y &= -2x - 2 \quad \text{(Subtracting $$2x$$ from both sides)} \
y &= 2x + 2 \quad \text{(Multiplying both sides by $$-1$$)}
\end{align*}
$$

**Simplified Equation:**
$$ y = 2x + 2 $$

### Step 2: Find the Intercepts

#### $$ x $$-Intercept:
The $$ x $$-intercept occurs where $$ y = 0 $$.

$$
\begin{align*}
0 &= 2x + 2 \
2x &= -2 \
x &= -1
\end{align*}
$$

**$$ x $$-Intercept:** $$(-1, 0)$$

#### $$ y $$-Intercept:
The $$ y $$-intercept occurs where $$ x = 0 $$.

$$
\begin{align*}
y &= 2(0) + 2 \
y &= 2
\end{align*}
$$

**$$ y $$-Intercept:** $$(0, 2)$$

### Step 3: Graph the Equation

To graph the equation $$ y = 2x + 2 $$, plot the two intercepts and draw a straight line through them.

1. **Plot the $$ y $$-intercept** at $$(0, 2)$$.
2. **Plot the $$ x $$-intercept** at $$(-1, 0)$$.
3. **Draw a straight line** passing through these two points.

Here's a simple representation of the graph:

```
y
|
4 |         *
3 |       *
2 |-----*---------
1 |    * 
0 |*------------
    -2 -1  0 1 2  x
```

- The point $$(0, 2)$$ is the $$ y $$-intercept.
- The point $$(-1, 0)$$ is the $$ x $$-intercept.
- The asterisks (*) represent points on the line $$ y = 2x + 2 $$.

### Summary

- **Simplified Equation:** $$ y = 2x + 2 $$
- **$$ x $$-Intercept:** $$(-1, 0)$$
- **$$ y $$-Intercept:** $$(0, 2)$$
- **Graph:** A straight line passing through $$(-1, 0)$$ and $$(0, 2)$$.

Feel free to plot these points on graph paper or use a graphing tool for a more accurate graph!
Simplify the equation $$ 2x - y = -2 $$ to $$ y = 2x + 2 $$. The $$ x $$-intercept is $$(-1, 0)$$ and the $$ y $$-intercept is $$(0, 2)$$. Graph the line by plotting these intercepts and drawing a straight line through them.

Simplify the equation if possible. Then graph the equation using the \( x \)-intercept and the \( y \)-interce \( 2 x-y=-2 \)

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