question 4 of 10

if you wanted to shift the graph of $y = 4x + 7$ down, which equation could you use?

a. $y = 4x + 11$
b. $y = x + 7$
c. $y = 4x + 3$
d. $y = -4x + 7$

Question

question 4 of 10

if you wanted to shift the graph of $y = 4x + 7$ down, which equation could you use?

a. $y = 4x + 11$
b. $y = x + 7$
c. $y = 4x + 3$
d. $y = -4x + 7$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Vertical Translation of Linear Functions" ], "new_concepts": [], "current_concepts": [ "Vertical Translation of Linear Functions", "Slope-Intercept Form" ] } ## Identify the original function and translation rule $$ \begin{aligned} &y = f(x) = 4x + 7\ &y_{\text{shifted}} = f(x) - k,\quad k > 0 \end{aligned} $$ ## Apply the vertical shift down $$ \begin{aligned} &y_{\text{shifted}} = 4x + 7 - k\ &y_{\text{shifted}} = 4x + c,\quad c < 7 \end{aligned} $$ ## Compare with the given options $$ \begin{aligned} &\text{Option A: } y = 4x + 11 \quad (11 > 7, \text{ shifted up})\ &\text{Option B: } y = x + 7 \quad (\text{slope changed})\ &\text{Option C: } y = 4x + 3 \quad (3 < 7, \text{ shifted down by } 4 \text{ units})\ &\text{Option D: } y = -4x + 7 \quad (\text{slope changed}) \end{aligned} $$

A. $y = 4x + 11$

B. $y = x + 7$

C. $y = 4x + 3$

D. $y = -4x + 7$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Vertical Translation of Linear Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the original function and translation rule

Apply the vertical shift down

Compare with the given options

Answer: