Question

find the slope of the line passing through the pair of points or state that the slope is undefined. then indicate whether the line through the points rises, falls, is horizontal, or is vertical.

\\((-3, 1)\\) and \\((2, 2)\\)

select the correct choice below and, if necessary, fill in the answer box within your choice.

a. the slope is \\(\square\\) (simplify your answer.)
b. the slope is undefined.

indicate whether the line through the points rises, falls, is horizontal, or is vertical.

a. the line falls from left to right.
b. the line is vertical.
c. the line is horizontal.
d. the line rises from left to right.

Explanation:

Identify the given points

Using the Slope Formula knowledge point

$$ (x_1, y_1) = (-3, 1), \quad (x_2, y_2) = (2, 2) $$

Calculate the slope

Using the Slope Formula knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 1}{2 - (-3)} = \frac{1}{5} $$

Determine the behavior of the line

Since the calculated slope \(m = \frac{1}{5}\) is positive (\(m > 0\)), the line rises from left to right.

Answer:

Question 1

• (A) The slope is <blank>\(\frac{1}{5}\)</blank> (Simplify your answer.) (Correct answer)
• (B) The slope is undefined

Question 2

• (A) The line falls from left to right.
• (B) The line is vertical.
• (C) The line is horizontal.
• (D) The line rises from left to right. (Correct answer)