if you wanted to make the graph of $y = 6x + 7$ less steep, which equation could you use?

a. $y = 6x + 4$
b. $y = 2x + 7$
c. $y = -6x + 7$
d. $y = 10x + 7$

Question

if you wanted to make the graph of $y = 6x + 7$ less steep, which equation could you use?

a. $y = 6x + 4$
b. $y = 2x + 7$
c. $y = -6x + 7$
d. $y = 10x + 7$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Slope Interpretation" ], "new_concepts": [ "Linear Function Steepness" ], "current_concepts": [ "Slope-Intercept Form", "Slope Interpretation", "Linear Function Steepness" ] } ## Identify the slope of the original line $$ \begin{aligned} &y = mx + b \ &y = 6x + 7 \implies m_{\text{original}} = 6 \end{aligned} $$ ## Define the condition for a less steep line $$ \begin{aligned} &|m_{\text{new}}| < |m_{\text{original}}| \ &|m_{\text{new}}| < 6 \end{aligned} $$ ## Evaluate the slopes of the given options $$ \begin{aligned} &\text{A. } y = 6x + 4 \implies |m| = 6 \ &\text{B. } y = 2x + 7 \implies |m| = 2 < 6 \ &\text{C. } y = -6x + 7 \implies |m| = 6 \ &\text{D. } y = 10x + 7 \implies |m| = 10 > 6 \end{aligned} $$

A. $y = 6x + 4$

B. $y = 2x + 7$

C. $y = -6x + 7$

D. $y = 10x + 7$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Function Steepness" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the slope of the original line

Define the condition for a less steep line

Evaluate the slopes of the given options

Answer: