Question

sketch a graph of the linear equation.
-2x-y=2

Answer 1

To sketch the graph of the linear equation \(-2x - y = 2\), we can rearrange the equation into the slope-intercept form \(y = mx + b\).

1. **Rearrange the equation**:
\[
-y = 2 + 2x
\]
\[
y = -2x - 2
\]

Here, the slope \(m\) is \(-2\) and the y-intercept \(b\) is \(-2\).

2. **Identify key points**:
- The y-intercept is at the point \((0, -2)\).
- To find another point, we can choose \(x = 1\):
\[
y = -2(1) - 2 = -2 - 2 = -4
\]
So, another point is \((1, -4)\).

- To find another point, we can choose \(x = -1\):
\[
y = -2(-1) - 2 = 2 - 2 = 0
\]
So, another point is \((-1, 0)\).

3. **Plot the points**:
- Plot the points \((0, -2)\), \((1, -4)\), and \((-1, 0)\) on a graph.

4. **Draw the line**:
- Draw a straight line through the points.

The graph is a straight line that slopes downward from left to right, starting from the y-intercept at \((0, -2)\) and passing through the other points.

Here’s a rough representation of what the graph would look like:

```
y
|
| • (-1, 0)
| •
| •
| • (0, -2)
|_________________________________ x
• (1, -4)
```

Feel free to use graphing tools or graph paper to create a more precise graph!