Question

watch the video and answer the question.
in the video, different slopes are summarized. what is the difference between zero slope and undefined slope? what does
o slope\ mean?
choose the correct answer.
◯ a. zero slope indicates ( m = 0 ) and a vertical line; undefined slope indicates ( m ) is undefined and a horizontal line; no slope refers to an undefined slope.
◯ b. zero slope indicates ( m = 0 ) and a horizontal line; undefined slope indicates ( m ) is undefined and a vertical line; no slope refers to an undefined slope.
◯ c. zero slope indicates ( m ) is undefined and a horizontal line; undefined slope indicates ( m = 0 ) and a vertical line; no slope refers to an undefined slope.
◯ d. zero slope indicates ( m = 0 ) and a horizontal line; undefined slope indicates ( m ) is undefined and a vertical line; no slope refers to ( m = 0 ).

Explanation:

Step1: Recall slope definitions

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a horizontal line, \(y_2=y_1\), so \(m = 0\). For a vertical line, \(x_2=x_1\), and the denominator in the slope formula is \(0\), making the slope undefined.

Step2: Analyze each option

• Option A: Zero slope (\(m = 0\)) is for horizontal lines, undefined slope (vertical line). But the description in A has wrong associations.
• Option B: Zero slope (\(m = 0\)) is for horizontal lines (correct), undefined slope (vertical line, correct).
• Option C: Mixes up the associations of zero and undefined slopes with line types.
• Option D: Incorrectly describes the relationship between slope values and line types.

Answer:

B. Zero slope indicates \(m = 0\) and a horizontal line; undefined slope indicates \(m\) is undefined and a vertical line.