Question

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

"y" equals negative 2 thirds "x" plus 5y=−
2
3​x+5

Answer 1

To identify the slope and y-intercept from the equation \( y = -\frac{2}{3}x + 5 \), we can follow these steps:

1. **Identify the slope (\( m \))**: In the equation of the form \( y = mx + b \), \( m \) is the slope. Here, \( m = -\frac{2}{3} \).

2. **Identify the y-intercept (\( b \))**: In the equation \( y = mx + b \), \( b \) is the y-intercept, which is the value of \( y \) when \( x = 0 \). Here, \( b = 5 \).

### Summary:
- **Slope (m)**: \( -\frac{2}{3} \)
- **y-intercept (b)**: \( 5 \)

### Graphing the Linear Equation:
1. **Plot the y-intercept**: Start by plotting the point where the line crosses the y-axis, which is at \( (0, 5) \).

2. **Use the slope to find another point**: The slope of \( -\frac{2}{3} \) means that for every 3 units you move to the right (positive direction on the x-axis), you move down 2 units (negative direction on the y-axis).

From the y-intercept \( (0, 5) \):
- Move 3 units to the right (to \( x = 3 \))
- Move 2 units down (from \( y = 5 \) to \( y = 3 \))
- This gives you the second point \( (3, 3) \).

3. **Draw the line**: Once you have the two points \( (0, 5) \) and \( (3, 3) \), draw a straight line through these points to represent the linear equation.

### Visualization:
If you were to graph it, you would have points marked at \( (0, 5) \) and \( (3, 3) \) along with a line connecting them, extending in both directions.

Here's a simple ASCII representation of the graph:

```
|
5 | *
| /
4 | /
| /
3 | *
| /
2 | /
| /
1 | /
| /
0 |________________
0 1 2 3 4
```

The asterisks (*) represent the points on the line.