Question

the line with a slope of 1/3 and a y- intercept of - 15 intersects the line passing through which of these pairs of points?

Answer 1

Answer:

Options (C), (D) and (E)

Step-by-step explanation:

Slope of the given line = $\frac{1}{3}$

Any line having same slope will be parallel to the given line otherwise the lines will intersect.

Therefore, we will find the slope of the lines passing through two points given in the options.

Option A

Slope of the line passing through (12, -13) and (15, -12)

m = $\frac{y_2-y_1}{x_2-x_1}$

   = $\frac{-13+12}{12-15}$

   = $\frac{1}{3}$

Therefore, both the lines are parallel having no point of intersection.

Option B

Slope = $\frac{-9+7}{18-24}$

          = $\frac{1}{3}$

Both the lines are parallel having no point of intersection.

Option C

Slope = $\frac{-20+21}{15-18}$

          = $-\frac{1}{3}$

Therefore, both the lines will intersect.

Option D

Slope = $\frac{-15+14}{30-36}$

          = $\frac{1}{6}$

Both the lines will intersect each other.

Option E

Slope = $\frac{-11+10}{24-30}$

          = $\frac{1}{6}$

Both the lines will intersect each other at a point.

Options (C), (D) and (E) are the correct options.