Question

Which graph contains the point (−5, 8) ? Responses - image with description: A graph of x versus y ranges from negative 10 to 10 in increments of 1 on both axes. A point is shown at 5 increments on the x-axis and 8 increments on the y-axis in quadrant 2. - - no response given - image with description: A graph of x versus y ranges from negative 10 to 10 in increments of 1 on both axes. A point is shown at 5 increments on the x-axis and 8 increments on the y-axis in quadrant 4. - - no response given - image with description: A graph of x versus y ranges from negative 10 to 10 in increments of 1 on both axes. A point is shown at 5 increments on the x-axis and 8 increments on the y-axis in quadrant 3. - - no response given

Answer 1

To determine which graph contains the point (−5, 8), we need to identify the coordinates:

- The x-coordinate is -5.
- The y-coordinate is 8.

We can break down the quadrants on a standard Cartesian plane:

- Quadrant I: x > 0, y > 0
- Quadrant II: x < 0, y > 0
- Quadrant III: x < 0, y < 0
- Quadrant IV: x > 0, y < 0

Since the x-coordinate is -5 (which is less than 0) and the y-coordinate is 8 (which is greater than 0), the point (−5, 8) is located in Quadrant II.

Now, let’s analyze the options based on the description provided:

1. **First Graph:** Described as having a point in Quadrant II at (5, 8) - **(incorrect, since it is not at -5, 8)**
2. **Second Graph:** Described as having a point in Quadrant IV at (5, 8) - **(incorrect, since it is not in Quadrant IV)**
3. **Third Graph:** Described as having a point in Quadrant III at (5, 8) - **(incorrect, since it is not in Quadrant III)**

None of the descriptions provided align with containing the point (−5, 8).

None of the graphs listed correctly show the point (−5, 8) since they do not capture the correct quadrant or coordinates. If they had included a point in Quadrant II at (−5, 8), that would be the correct choice.