a line passes through the point (0, -1) and has a positive slope. which of these points could that line pass…

Explanation:

Step1: Recall the slope formula

The slope formula is (m=\frac{y_2 - y_1}{x_2 - x_1}), where ((x_1,y_1)=(0,-1)) and ((x_2,y_2)) is the other point.

Step2: Calculate slope for ((12,3))

(m=\frac{3-(-1)}{12 - 0}=\frac{4}{12}=\frac{1}{3}>0)

Step3: Calculate slope for ((-2,-5))

(m=\frac{-5-(-1)}{-2 - 0}=\frac{-4}{-2}=2>0)

Step4: Calculate slope for ((-3,1))

(m=\frac{1-(-1)}{-3 - 0}=\frac{2}{-3}=-\frac{2}{3}<0)

Step5: Calculate slope for ((1,15))

(m=\frac{15-(-1)}{1 - 0}=\frac{16}{1}=16>0)

Step6: Calculate slope for ((5,-2))

(m=\frac{-2-(-1)}{5 - 0}=\frac{-1}{5}=-\frac{1}{5}<0)

Answer:

((12,3)), ((-2,-5)), ((1,15))