Question

A coordinate plane. A line passes through the point (0, 1) and has a positive slope. Which of these points could that line NOT pass through? Check all that apply.

A. (12, 3)
B. (–2, –5)
C. (–3, 1)
D. (1, 15)
E. (5, –2)

Answer 1

A line with a positive slope passing through (0, 1) cannot pass through point C. (–3, 1) since the y-value does not decrease when x < 0, and E. (5, –2) since the y-value should be greater than 1 when x > 0.

Step-by-step explanation:

A line with a positive slope means that as the x-coordinate increases, the y-coordinate also increases. Given a line passes through the point (0, 1), for any other point (x, y) on this line with x > 0, y must be greater than 1, and for x < 0, y must be less than 1. Therefore, we need to check which points do not satisfy this condition based on the provided options.

1. (12, 3) - This point could be on the line as it has x > 0 and y > 1.
2. (–2, –5) - This point could also be on the line as it has x < 0 and y < 1.
3. (–3, 1) - This point could not be on the line since y does not decrease when x < 0.
4. (1, 15) - This point could be on the line as it has x > 0 and y > 1.
5. (5, –2) - This point could not be on the line since y < 1 when it should be greater for x > 0.

The points that a line with a positive slope passing through (0, 1) could NOT pass through are C. (–3, 1) and E. (5, –2).