a line passes through the point (0, 1) and has a positive slope. which of these points could that line not…

Answer:

C. (-3, 1), E. (5, -2)

Explanation:

Step1: Recall slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. The line passes through $(0,1)$.

Step2: Calculate slope for (12,3)

$m=\frac{3 - 1}{12-0}=\frac{2}{12}=\frac{1}{6}>0$. So the line could pass through (12,3).

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

$m=\frac{-5 - 1}{-2-0}=\frac{-6}{-2}=3>0$. So the line could pass through (-2,-5).

Step4: Calculate slope for (-3,1)

$m=\frac{1 - 1}{-3-0}=0$. Since the line has a positive slope, it could not pass through (-3,1).

Step5: Calculate slope for (1,15)

$m=\frac{15 - 1}{1-0}=14>0$. So the line could pass through (1,15).

Step6: Calculate slope for (5,-2)

$m=\frac{-2 - 1}{5-0}=\frac{-3}{5}<0$. Since the line has a positive slope, it could not pass through (5,-2).