question 5 of 10

which of the following are the correct properties of slope?

check all that apply.

a. the slope of a steep line with a positive slope should be smaller than the slope of a flat line.
b. lines that go up from left to right should have a positive slope.
c. lines that go down from left to right should have a negative slope.
d. the slope of a steep line with a positive slope should be bigger than the slope of a flat line.
e. lines that have positive slopes and are equally steep should have the same slope.

Question

question 5 of 10

which of the following are the correct properties of slope?

check all that apply.

a. the slope of a steep line with a positive slope should be smaller than the slope of a flat line.
b. lines that go up from left to right should have a positive slope.
c. lines that go down from left to right should have a negative slope.
d. the slope of a steep line with a positive slope should be bigger than the slope of a flat line.
e. lines that have positive slopes and are equally steep should have the same slope.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "direct_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Interpretation" ], "new_concepts": [], "current_concepts": [ "Slope Interpretation", "Properties of Slope" ] } ## Analyze direction-based slope properties $$ \begin{aligned} &\text{Left-to-right upward lines} \implies m > 0 \quad (\text{Statement B is true}) \ &\text{Left-to-right downward lines} \implies m < 0 \quad (\text{Statement C is true}) \end{aligned} $$ ## Analyze steepness-based slope properties $$ \begin{aligned} &\text{For } m > 0, \text{ steeper line} \implies \text{larger value of } m \quad (\text{Statement D is true, Statement A is false}) \ &\text{Equally steep lines with positive slopes} \implies \text{identical rise over run} \implies \text{same slope value} \quad (\text{Statement E is true}) \end{aligned} $$

(A) The slope of a steep line with a positive slope should be smaller than the slope of a flat line.

(B) Lines that go up from left to right should have a positive slope.

(C) Lines that go down from left to right should have a negative slope.

(D) The slope of a steep line with a positive slope should be bigger than the slope of a flat line.

(E) Lines that have positive slopes and are equally steep should have the same slope.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Slope Interpretation" ] }

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Question

Explanation:

Analyze direction-based slope properties

Analyze steepness-based slope properties

Answer: