Creating a Line with a Positive Slope A line passes through the point (0, -1) and has a positive slope. Which of these points could the line pass through? Check all that apply. (12, 3) (-2, -5) (-3, 1) (1, 15) (5, -2)
Mathematics · Middle School · Thu Feb 04 2021
Answered on
To check if a point is on a line with a positive slope that passes through (0, -1), we need to determine if moving from (0, -1) to each point reflects a positive rise for each positive run (if moving to the right on the x-axis). For a line with a positive slope, as we move to the right (increase in x), the y-value should also increase.
1. Point (12, 3): Moving from (0, -1) to (12, 3), the run is 12 (since 12 - 0 = 12) and the rise is 4 (since 3 - (-1) = 3 + 1 = 4). Both are positive, indicating a positive slope. So, this point could be on the line.
2. Point (-2, -5): Moving from (0, -1) to (-2, -5), the run is -2 (since -2 - 0 = -2) and the rise is -4 (since -5 - (-1) = -5 + 1 = -4). Both are negative, which would imply a positive slope; however, we are moving to the left (decrease in x), not the right, so this does not conform to our initial condition of positive slope with increasing x values. Therefore, this point could not be on the line.
3. Point (-3, 1): Moving from (0, -1) to (-3, 1), the run is -3 (since -3 - 0 = -3) and the rise is 2 (since 1 - (-1) = 1 + 1 = 2). The rise is positive, but since we are moving to the left with a negative run, this does not represent a positive slope for our line. Therefore, this point could not be on the line.
4. Point (1, 15): Moving from (0, -1) to (1, 15), the run is 1 (since 1 - 0 = 1) and the rise is 16 (since 15 - (-1) = 15 + 1 = 16), which are both positive, indicating a positive slope. So, this point could be on the line.
5. Point (5, -2): Moving from (0, -1) to (5, -2), the run is 5 (since 5 - 0 = 5) and the rise is -1 (since -2 - (-1) = -2 + 1 = -1), which indicates a negative slope since the y-value decreases with an increase in x-value. Therefore, this point could not be on the line.
Points that could be on the line with a positive slope passing through (0, -1) are (12, 3) and (1, 15).