Question

find the slope of the line passing through the pair of points below. assume that all variables represent positive real numbers. then indicate whether the line through the points rises, falls, is horizontal, or is vertical.

\\((a, b)\\) and \\((a, b + c)\\)

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

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

which of the following describes the line passing through the given points?

• vertical
• rises from left to right
• falls from left to right
• horizontal

Explanation:

Identify the given points

The two points given are:

$$ (x_1, y_1) = (a, b) $$

$$ (x_2, y_2) = (a, b + c) $$

where \(a\), \(b\), and \(c\) represent positive real numbers.

Apply the slope formula

Using the Vertical Lines knowledge point

$$
LATEXBLOCK0
$$

Since division by zero is undefined, the slope \(m\) is undefined.

Determine the behavior of the line

Using the Vertical Lines knowledge point

$$
LATEXBLOCK1
$$

Answer:

Question 1

• (A) The slope is [ ] (Simplify your answer.)
• (B) The slope is undefined (Correct answer)

Question 2

• Vertical (Correct answer)
• Rises from left to right
• Falls from left to right
• Horizontal