Question

Which equations could represent this graph? Choose all that apply.



(2 points)
Responses

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

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

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

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

y = 5x + 8

Answer 1

To determine which equations could represent the graph, we need to assess the slope and y-intercept of each equation and compare them with the characteristics of the given graph.

Here are the equations reviewed:

1. **y = -2/3x + 5**: This has a negative slope (-2/3) and a y-intercept of 5.

2. **2x + 3y = 15**: Rearranging into slope-intercept form (y = mx + b):
\[
3y = -2x + 15 \implies y = -\frac{2}{3}x + 5
\]
This has the same slope and intercept as the first equation, so it is equivalent.

3. **-3x + 2y = 5**: Rearranging into slope-intercept form:
\[
2y = 3x + 5 \implies y = \frac{3}{2}x + \frac{5}{2}
\]
This has a positive slope (3/2) and is unlikely to match with a graph with a negative slope.

4. **y = 5x - 2**: This has a positive slope (5) and a negative y-intercept (-2). This will not match with any negative slope graph.

5. **y = 5x + 8**: This also has a positive slope (5) and a positive y-intercept (8), which again does not match with any negative slope graph.

Based on this analysis:

- The equations that could represent the graph, assuming it has a negative slope and an intercept of 5, are:
- **y = -2/3x + 5**
- **2x + 3y = 15**

The equations that do not match are:
- **-3x + 2y = 5**
- **y = 5x - 2**
- **y = 5x + 8**

Final answer: y = -2/3x + 5 and 2x + 3y = 15.