$$ 1 \leftarrow \quad \begin{array}{l} ext { Simplity the equation if possible. Find the } x ext {-intercept and the } y ext {-intercept. Then graph the equation. } \ -2 x-7 y=7\end{array} $$

Question

$$ 1 \leftarrow \quad \begin{array}{l}	ext { Simplity the equation if possible. Find the } x 	ext {-intercept and the } y 	ext {-intercept. Then graph the equation. } \ -2 x-7 y=7\end{array} $$

UpStudy AI · Accepted Answer

Sure, let's work through the problem step by step.

### Given Equation:
$$
-2x - 7y = 7
$$

### 1. Simplify the Equation

We can rewrite the equation in the slope-intercept form ($$ y = mx + b $$) to make it easier to graph.

$$
-2x - 7y = 7
$$

**Step 1:** Isolate the $$ y $$-term.

$$
-7y = 2x + 7
$$

**Step 2:** Divide both sides by $$-7$$ to solve for $$ y $$.

$$
y = -\frac{2}{7}x - 1
$$

So, the simplified equation is:
$$
y = -\frac{2}{7}x - 1
$$

### 2. Find the Intercepts

**a. $$ x $$-Intercept:**

The $$ x $$-intercept occurs where $$ y = 0 $$.

$$
-2x - 7(0) = 7 \
-2x = 7 \
x = -\frac{7}{2}
$$

**$$ x $$-Intercept:** $$ \left( -\frac{7}{2},\ 0 \right) $$ or $$ (-3.5,\ 0) $$

**b. $$ y $$-Intercept:**

The $$ y $$-intercept occurs where $$ x = 0 $$.

$$
-2(0) - 7y = 7 \
-7y = 7 \
y = -1
$$

**$$ y $$-Intercept:** $$ \left( 0,\ -1 \right) $$

### 3. Graph the Equation

To graph the equation $$ y = -\frac{2}{7}x - 1 $$:

1. **Plot the $$ y $$-Intercept:**
   - Start by plotting the point $$ (0, -1) $$ on the graph.

2. **Plot the $$ x $$-Intercept:**
   - Plot the point $$ (-3.5, 0) $$.

3. **Draw the Line:**
   - Draw a straight line passing through both intercepts. This line represents all the solutions to the equation $$ -2x - 7y = 7 $$.

4. **Slope Interpretation:**
   - The slope $$ m = -\frac{2}{7} $$ indicates that for every 7 units you move to the right along the $$ x $$-axis, you move 2 units down.

### Graph Illustration

Since I can't provide a visual graph here, follow these steps to draw it:

1. **Draw the Coordinate Axes:**
   - Draw a horizontal line for the $$ x $$-axis and a vertical line for the $$ y $$-axis intersecting at the origin $$ (0, 0) $$.

2. **Mark the Intercepts:**
   - Plot $$ (0, -1) $$ on the $$ y $$-axis.
   - Plot $$ (-3.5, 0) $$ on the $$ x $$-axis.

3. **Draw the Line:**
   - Use a ruler to draw a straight line that passes through both intercept points.
   - Extend the line in both directions and add arrows to indicate it continues indefinitely.

4. **Label the Axes:**
   - Clearly label the $$ x $$-axis and $$ y $$-axis.
   - Optionally, add the equation $$ y = -\frac{2}{7}x - 1 $$ near the line for reference.

### Summary

- **Simplified Equation:** $$ y = -\frac{2}{7}x - 1 $$
- **$$ x $$-Intercept:** $$ \left( -\frac{7}{2},\ 0 \right) $$
- **$$ y $$-Intercept:** $$ \left( 0,\ -1 \right) $$
- **Graph:** A straight line passing through $$ (-3.5, 0) $$ and $$ (0, -1) $$ with a slope of $$ -\frac{2}{7} $$.

If you follow these steps, you'll have successfully graphed the equation $$ -2x - 7y = 7 $$.
Simplify the equation to $$ y = -\frac{2}{7}x - 1 $$. The $$ x $$-intercept is at $$ (-3.5, 0) $$ and the $$ y $$-intercept is at $$ (0, -1) $$. Graph the line passing through these points with a slope of $$ -\frac{2}{7} $$.

\( 1 \leftarrow \quad \begin{array}{l}\text { Simplity the equation if possible. Find the } x \text {-intercept and the } y \text {-intercept. Then graph the equation. } \\ -2 x-7 y=7\end{array} \)

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