Question

Identify the slope and y intercept. Then, graph the linear equation.

`y-6=-2x`

Answer 1

To identify the slope and y-intercept from the equation \(y - 6 = -2x\), we'll first rewrite it in the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the given equation:

\[ y - 6 = -2x \]

Add 6 to both sides to isolate \(y\):

\[ y = -2x + 6 \]

From this equation, we can identify:

- The slope \(m = -2\)
- The y-intercept \(b = 6\)

This means the line slopes downwards (since the slope is negative) and crosses the y-axis at (0, 6).

### Graph the Linear Equation

1. **Plot the y-intercept**: Start by plotting the point (0, 6) on the y-axis.
2. **Use the slope to find another point**: The slope of -2 can be interpreted as: for every 1 unit you move to the right (positive x-direction), move 2 units down (negative y-direction).
- From (0, 6), if you move 1 unit to the right (to 1, 6) and then move down 2 units, you would end up at (1, 4).
3. **Plot this point**: So plot (1, 4).
4. **Draw the line**: Connect these two points with a straight line and extend it in both directions.

### Summary
- **Slope**: -2
- **Y-Intercept**: (0, 6)
- The graph will show a straight line passing through the y-axis at (0, 6) and having a downward slope.

You can visualize it as follows:

```
7 | * (0,6)
6 |
5 |
4 | * (1,4)
3 |
2 |
1 |
0 |________________
0 1 2 3 4 x
```

The line will continue to slope down as you move to the right.