122k views
1 vote
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 that line pass through?
Check all that apply.

A (12,3)
B (-2,-5)
C (-3, 1)
D (1, 15)
E (5,-2)

1 Answer

3 votes

Final Answer:

The line passing through (0, -1) and having a positive slope could pass through points (12,3), (-3, 1), and (1, 15). Thus the correct options are A, C and D.

Step-by-step explanation:

Given point:

(P(0, -1)

Equation of a line in point-slope form:

(y - y₁) = m(x - x₁), where (x₁, y₁) = (0, -1) and m represents the positive slope

Given positive slope:

Let's assume m = k (a positive value).

Now, let's test each point:

A (12, 3):

Substitute (x₁, y₁) = (0, -1) and the coordinates of point A into the point-slope equation:

3 - (-1) = k(12 - 0)

4 = 12k

k = 4/12 = 1/3

C (-3, 1):

Substitute (x₁, y₁) = (0, -1) and the coordinates of point C into the point-slope equation:

1 - (-1) = k(-3 - 0)

2 = -3k

k = 2/-3 = -2/3

D (1, 15):

Substitute (x₁, y₁) = (0, -1) and the coordinates of point D into the point-slope equation:

15 - (-1) = k(1 - 0)

16 = k

For points B (-2, -5) and E (5, -2), let's follow the same process:

B (-2, -5):

y - (-1) = k(-2 - 0)

-5 + 1 = -2k

-4 = -2k

k = -4/-2= 2

E (5, -2):

y - (-1) = k(5 - 0)

-2 + 1 = 5k

-1 = 5k

k = -1/5

From these calculations, the values of k for points A, C, and D are k = 1/3, k = -2/3, and k = 16 respectively. Only points A, C, and D result in positive or negative slopes as required, indicating that the line passing through the point (0, -1) with a positive slope can go through points A (12, 3), C (-3, 1), and D (1, 15).

Therefore, the correct options are A, C and D.

User Mojo
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories