Question

a line passes through the point (0, -1) and has a positive slope. which of these points could that line pass through? check all that apply. (12, 3) (-2, -5) (-3, 1) (1, 15) (5, -2)

Explanation:

Step1: Recall slope formula

Slope $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)=(0,-1)$

Step2: Calculate slope for (12,3)

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

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

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

Step4: Calculate slope for (-3,1)

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

Step5: Calculate slope for (1,15)

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

Step6: Calculate slope for (5,-2)

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

Step7: Select positive slopes

Keep points where $m>0$

Answer:

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