Question

identify the slope and y intercept. Then, graph the linear equation.
y = -2/3x + 5
Begin with B, the y-intercept: _____
Move with m, the slope: _____

Answer 1

how would u graph this

Answer 2

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

1. **Identify the y-intercept (B)**: The y-intercept is the value of \( y \) when \( x = 0 \). From the equation, the y-intercept is 5. Thus, \( B = 5 \). This point is (0, 5) on the graph.

2. **Identify the slope (m)**: The slope is given by the coefficient of \( x \), which in this case is \( -\frac{2}{3} \). Thus, \( m = -\frac{2}{3} \). This means that for every 3 units we move to the right (positive direction on the x-axis), we move 2 units down (negative direction on the y-axis).

### Steps to graph the linear equation:

1. **Plot the y-intercept (0, 5)**: Start at the point (0, 5) on the y-axis.

2. **Use the slope to find another point**:
- From (0, 5), move 3 units to the right (to (3, 5)) and then move 2 units down (to (3, 3)). This gives a second point at (3, 3).
- Alternatively, you can move 3 units to the left (to (-3, 5)) and 2 units up (to (-3, 7)), giving you another point at (-3, 7).

3. **Draw the line**: Connect the two points with a straight line extending in both directions.

### Summary:
- Y-intercept \( B = 5 \)
- Slope \( m = -\frac{2}{3} \)

You now have the equation graphed with the points (0, 5) and (3, 3) or (-3, 7).

Answer 3

To graph the linear equation \( y = -\frac{2}{3}x + 5 \), you can follow these steps:

### Step-by-Step Graphing Instructions

1. **Plot the Y-Intercept:**
- From the equation \( y = -\frac{2}{3}x + 5 \), the y-intercept is **5**.
- Plot the point at (0, 5) on the y-axis.

2. **Use the Slope to Find Another Point:**
- The slope of the line is \( -\frac{2}{3} \). This means for every **3** units you move to the right (in the positive direction), you move **2** units down (in the negative direction).
- Starting from the y-intercept (0, 5):
- Move **3 units right**: from \( x = 0 \) to \( x = 3 \).
- Move **2 units down**: from \( y = 5 \) to \( y = 3 \).
- This gives you the point (3, 3). Plot this point.

3. **Find Another Point Using Negative Slope:**
- Alternatively, you can move in the opposite direction:
- From (0, 5), move **3 units left**: from \( x = 0 \) to \( x = -3 \).
- Move **2 units up**: from \( y = 5 \) to \( y = 7 \).
- This gives you the point (-3, 7). Plot this point.

4. **Draw the Line:**
- Use a ruler to draw a straight line that passes through the points (0, 5), (3, 3), and (-3, 7).
- Extend the line in both directions, adding arrows at the ends to indicate that it continues indefinitely.

### Summary of Points:
- **Y-Intercept**: (0, 5)
- **Additional Point**: (3, 3)
- Another point: (-3, 7)

### Optional:
- Label the y-intercept and any additional points on your graph for clarity.
- Ensure that your graph has a proper scale on the axes for accuracy.

### Example of the Final Graph:
Here's a visual representation of how to graph it (described in text but normally drawn on paper):

```
|
7 | *
|
6 |
|
5 | *
|
4 |
|
3 | *
|
2 |
|
1 |
|
0 |________________________
0 1 2 3 4 5
```

In the above graph:
- The '*' marks indicate where the points are located.
- The slope moves down as you move from left to right, confirming that the slope is negative.

You’ll need to produce this graph on graph paper or using graphing software to visualize it properly!