activity - finding greater slope

value: 1

which function has greater slope?

a. $3x + 4y = 5$
b. $y = 9x - 9$
c. $y - 5 = 0$
d. $4y = 8x - 4$

Question

activity - finding greater slope

value: 1

which function has greater slope?

a. $3x + 4y = 5$
b. $y = 9x - 9$
c. $y - 5 = 0$
d. $4y = 8x - 4$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope of a Linear Function", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Slope of a Linear Function", "Slope-Intercept Form" ] } ## Convert equations to slope-intercept form $$ \begin{aligned} &\text{a. } 3x + 4y = 5 \implies 4y = -3x + 5 \implies y = -\frac{3}{4}x + \frac{5}{4} \implies m = -\frac{3}{4}\ &\text{b. } y = 9x - 9 \implies m = 9\ &\text{c. } y - 5 = 0 \implies y = 5 \implies m = 0\ &\text{d. } 4y = 8x - 4 \implies y = 2x - 1 \implies m = 2 \end{aligned} $$ ## Compare the slopes $$ \begin{aligned} &m_a = -0.75\ &m_b = 9\ &m_c = 0\ &m_d = 2\ &9 > 2 > 0 > -0.75 \end{aligned} $$

a. $3x + 4y = 5$

b. $y = 9x - 9$

c. $y - 5 = 0$

d. $4y = 8x - 4$

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

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QUESTION IMAGE

Question

Explanation:

Convert equations to slope-intercept form

Compare the slopes

Answer: