question 1 of 10

if (y = x + 5) were changed to (y = x + 9), how would the graph of the new function compare with the first one?

a. it would be shifted right.
b. it would be steeper.
c. it would be shifted down.
d. it would be shifted up.

Question

question 1 of 10

if (y = x + 5) were changed to (y = x + 9), how would the graph of the new function compare with the first one?

a. it would be shifted right.
b. it would be steeper.
c. it would be shifted down.
d. it would be shifted up.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Geometric Translation" ], "new_concepts": [ "Vertical Translation of Linear Functions" ], "current_concepts": [ "Slope-Intercept Form", "Geometric Translation", "Vertical Translation of Linear Functions" ] } ## Compare the slopes of the two linear functions $$ \begin{aligned} &m_1 = 1 \quad \text{for} \quad y = x + 5 \ &m_2 = 1 \quad \text{for} \quad y = x + 9 \ &m_1 = m_2 \end{aligned} $$ ## Compare the y-intercepts of the two linear functions $$ \begin{aligned} &b_1 = 5 \quad \text{for} \quad y = x + 5 \ &b_2 = 9 \quad \text{for} \quad y = x + 9 \ &b_2 - b_1 = 9 - 5 = 4 \end{aligned} $$ ## Determine the geometric transformation $$ y_{\text{new}} = y_{\text{old}} + 4 $$

A. It would be shifted right.

B. It would be steeper.

C. It would be shifted down.

D. It would be shifted up.

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QUESTION IMAGE

Question

Explanation:

Compare the slopes of the two linear functions

Compare the y-intercepts of the two linear functions

Determine the geometric transformation

Answer: