Question

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

`y=-\frac{2}{3}x+5`


it's not 0, 5 and 3, 3

Answer 1

To identify the slope and y-intercept from the linear equation \( y = -\frac{2}{3}x + 5 \):

1. **Slope (m)**: The coefficient of \( x \) is the slope. In this case, the slope \( m = -\frac{2}{3} \).

2. **Y-intercept (b)**: This is the constant term in the equation, which is the value of \( y \) when \( x = 0 \). Here, the y-intercept \( b = 5 \).

So, the slope is \( -\frac{2}{3} \) and the y-intercept is \( 5 \).

### Graphing the Linear Equation

To graph the equation \( y = -\frac{2}{3}x + 5 \):

1. **Plot the y-intercept**: Start by plotting the point (0, 5) on the graph.

2. **Using the slope**: The slope \( -\frac{2}{3} \) means that for every 3 units you move to the right (positive x-direction), you will move down 2 units (negative y-direction).

- From (0, 5), move 3 units right to \( x = 3 \), and then move down 2 units to get to (3, 3). Plot this point.

3. **Draw the line**: Draw a straight line through the points (0, 5) and (3, 3) extending in both directions.

### Points to Plot:

1. \( (0, 5) \) (y-intercept)
2. \( (3, 3) \) (calculated using the slope)

### Sketch of the Graph

Here is a description of how the line might look:

- The line will start at the point (0, 5) on the y-axis and will slope downward due to the negative slope.
- When you reach (3, 3), you can see that the line decreases as it moves to the right.

The graph would appear as follows:

```
y
↑
|
| ● (0,5)
| ●
| ●
| ●
| ●
| ●
+------------------→ x
```

In this sketch:
- The point (0, 5) is marked, and the line decreases as it moves to the right, consistent with the slope of \( -\frac{2}{3} \).