Question

Which equations could represent this graph? Choose all that apply.
y = -2/3x + 5
y = -2/3x + 5

y = 5x - 2
y = 5x - 2

2x + 3y = 15
2x + 3y = 15

-3x + 2y = 5
-3x + 2y = 5

y = 5x + 8

Answer 1

To determine which equations could represent the graph you're referring to, we need to analyze the provided equations. However, since I cannot see the graph, I will help you evaluate the equations based on their slopes and y-intercepts.

1. **y = -2/3x + 5**
- Slope: -2/3
- Y-intercept: 5

2. **y = 5x - 2**
- Slope: 5
- Y-intercept: -2

3. **2x + 3y = 15**
- Rearranged to slope-intercept form:
- 3y = -2x + 15
- y = -2/3x + 5
- Slope: -2/3
- Y-intercept: 5

4. **-3x + 2y = 5**
- Rearranged to slope-intercept form:
- 2y = 3x + 5
- y = (3/2)x + 5/2
- Slope: 3/2
- Y-intercept: 5/2

5. **y = 5x + 8**
- Slope: 5
- Y-intercept: 8

### Summary:
- **y = -2/3x + 5** and **2x + 3y = 15** are equivalent and have the same slope and y-intercept.
- **y = 5x - 2** and **y = 5x + 8** have a slope of 5.
- **-3x + 2y = 5** has a different slope and intercept.

To choose which equations could represent the graph, consider the slope and y-intercept you see in the graph:

- If the graph has a slope of -2/3 and a y-intercept of 5, select **y = -2/3x + 5** and **2x + 3y = 15**.
- If the graph has a slope of 5, select **y = 5x - 2** and **y = 5x + 8**.

Without knowing the specifics of the graph, you would select the equations based on the characteristics observed in the graph.