Question
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A line passes through the point (0, 1)
and has a positive slope. Which of these points could that line NOT pass through. Select the two that apply.
(2 points)
Responses
(5, −2)
(5, −2)
(1, 15)
(1, 15)
(12, 3)
(12, 3)
(−2, −5)
(−2, −5)
(−3, 1)
A line passes through the point (0, 1)
and has a positive slope. Which of these points could that line NOT pass through. Select the two that apply.
(2 points)
Responses
(5, −2)
(5, −2)
(1, 15)
(1, 15)
(12, 3)
(12, 3)
(−2, −5)
(−2, −5)
(−3, 1)
Answers
GPT-4o mini
To determine which points a line with a positive slope passing through (0, 1) could NOT go through, we can analyze the y-values of the given points in relation to their x-values.
A line with a positive slope means that as x increases, y also increases. Therefore, we need to check the relationship between the x and y coordinates of each point compared to the line.
1. **(5, -2)**: The x-value is 5 and the y-value is -2. Since -2 is less than 1 (the y-value at x=0), a line with a positive slope cannot pass through this point.
2. **(1, 15)**: Here, the x-value is 1 and the y-value is 15, which is greater than 1. This point is on the line since as x increases from 0 to 1, y also increases from 1 to 15.
3. **(12, 3)**: The x-value is 12 and the y-value is 3, which is also greater than 1. Thus, this point can be on the line with positive slope.
4. **(−2, -5)**: The x-value is -2 and the y-value is -5, which is less than 1. This point cannot be on the line either.
5. **(−3, 1)**: The x-value is -3 and the y-value is 1, which is the same as the y-value at x=0. Therefore, it is possible for the line to pass through this point.
Therefore, the two points that the line with a positive slope passing through (0, 1) could NOT pass through are:
- (5, -2)
- (−2, -5)
A line with a positive slope means that as x increases, y also increases. Therefore, we need to check the relationship between the x and y coordinates of each point compared to the line.
1. **(5, -2)**: The x-value is 5 and the y-value is -2. Since -2 is less than 1 (the y-value at x=0), a line with a positive slope cannot pass through this point.
2. **(1, 15)**: Here, the x-value is 1 and the y-value is 15, which is greater than 1. This point is on the line since as x increases from 0 to 1, y also increases from 1 to 15.
3. **(12, 3)**: The x-value is 12 and the y-value is 3, which is also greater than 1. Thus, this point can be on the line with positive slope.
4. **(−2, -5)**: The x-value is -2 and the y-value is -5, which is less than 1. This point cannot be on the line either.
5. **(−3, 1)**: The x-value is -3 and the y-value is 1, which is the same as the y-value at x=0. Therefore, it is possible for the line to pass through this point.
Therefore, the two points that the line with a positive slope passing through (0, 1) could NOT pass through are:
- (5, -2)
- (−2, -5)