Question

Creating a Line with a Positive Slope
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.
(12, 3)
(–2, –5)
(–3, 1)
(1, 15)
(5, –2)

Answer 1

A line through (0, 1) has slope m = (y − 1)/x. For m > 0 we need x(y − 1) > 0 (x and y − 1 have the same sign).

Check each point:
- (12, 3): x( y − 1) = 12·2 > 0 → possible.
- (−2, −5): (−2)·(−6) > 0 → possible.
- (−3, 1): (−3)·0 = 0 → slope 0 (not positive) → NOT possible.
- (1, 15): 1·14 > 0 → possible.
- (5, −2): 5·(−3) < 0 → slope negative → NOT possible.

So the line could NOT pass through (−3, 1) and (5, −2).