Question

18. 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

y = 5x + 8
y = 5x + 8

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

y = 5x - 2
y = 5x - 2
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Answer 1

To determine which equations may represent the given graph, we need to analyze each equation to find its slope and y-intercept, and then compare those characteristics to the graph.

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

2. **2x + 3y = 15**
- Rearranging to slope-intercept form (y = mx + b):
- 3y = -2x + 15
- y = -2/3x + 5
- Slope: -2/3
- Y-intercept: 5

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

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

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

To identify which graphs could match the described graph, we check each one for matching slopes and y-intercepts with the graph data. If the slopes and y-intercepts match visually with the graph provided, then these equations would apply.

Based on the analysis above:
- **y = -2/3x + 5** and **2x + 3y = 15** represent the same line and could both represent part of the graph.
- The other three equations have different slopes and y-intercepts that do not match the properties of the first two lines.

Therefore, the correct responses are:
- **y = -2/3x + 5**
- **2x + 3y = 15**