this table represents a linear function.

$\begin{array}{|c|c|}\hline x & y \\\hline 0 & 5 \\\hline 5 & 15 \\\hline\end{array}$

this graph represents another function.

the greater unit rate of the two functions is choose an answer. the greater $y$-intercept of the two functions is choose an answer.

Question

this table represents a linear function.

$\begin{array}{|c|c|}\hline x & y \\\hline 0 & 5 \\\hline 5 & 15 \\\hline\end{array}$

this graph represents another function.

the greater unit rate of the two functions is choose an answer. the greater $y$-intercept of the two functions is choose an answer.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Rate of Change", "Y-intercept Interpretation" ], "new_concepts": [], "current_concepts": [ "Rate of Change", "Y-intercept Interpretation", "Linear Function Interpretation", "Rate of Change Comparison" ] } ## Find the rate of change and y-intercept of the table function Using the *Rate of Change* and *Y-intercept Interpretation* knowledge points $$ \begin{aligned} &\text{Rate of change (unit rate)} = \frac{15 - 5}{5 - 0} = \frac{10}{5} = 2\ &\text{y-intercept} = 5 \quad (\text{since } y = 5 \text{ when } x = 0) \end{aligned} $$ ## Find the rate of change and y-intercept of the graph function Using the *Rate of Change* and *Y-intercept Interpretation* knowledge points $$ \begin{aligned} &\text{y-intercept} = 6 \quad (\text{the line crosses the y-axis at } (0, 6))\ &\text{x-intercept} = -4 \quad (\text{the line crosses the x-axis at } (-4, 0))\ &\text{Rate of change (unit rate)} = \frac{6 - 0}{0 - (-4)} = \frac{6}{4} = 1.5 \end{aligned} $$ ## Compare the unit rates and y-intercepts Using the *Rate of Change* and *Y-intercept Interpretation* knowledge points $$ \begin{aligned} &\text{Unit rates: } 2 > 1.5 \implies \text{Greater unit rate is } 2\ &\text{y-intercepts: } 6 > 5 \implies \text{Greater y-intercept is } 6 \end{aligned} $$ The greater unit rate of the two functions is 2. The greater y-intercept of the two functions is 6. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Rate of Change Comparison" ] }

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QUESTION IMAGE

Question

Explanation:

Find the rate of change and y-intercept of the table function

Find the rate of change and y-intercept of the graph function

Compare the unit rates and y-intercepts

Answer: