select the correct answer from each drop-down menu.

a manufacturing company produces engines for light aircraft. the graph shows the number of engines produced each year since the company started operations.

engine production

the data plot can be represented by the function choose an answer.
based on the scatter plot, we can predict that in the choose an answer year, the company will produce choose an answer engines.

options for the first drop-down:
- $10x + 35$
- $20x + 40$
- $2x + 40$
- $13x + 32$

Question

select the correct answer from each drop-down menu.

a manufacturing company produces engines for light aircraft. the graph shows the number of engines produced each year since the company started operations.

engine production

the data plot can be represented by the function choose an answer.
based on the scatter plot, we can predict that in the choose an answer year, the company will produce choose an answer engines.

options for the first drop-down:
- $10x + 35$
- $20x + 40$
- $2x + 40$
- $13x + 32$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Line of Best Fit Selection", "Line of Best Fit Prediction" ], "new_concepts": [], "current_concepts": [ "Line of Best Fit Selection", "Line of Best Fit Prediction", "Scatter Plot Analysis" ] } ## Determine the line of best fit from the options $$ \begin{aligned} &\text{Let } x \text{ be the number of years and } y \text{ be the number of engines produced.}\ &\text{From the scatter plot, estimate key data points } (x, y):\ &(1, 48), (2, 62), (3, 78), (4, 90), (5, 104), (6, 120), (7, 134), (8, 148)\ &\text{Calculate the approximate slope } m \approx \frac{148 - 48}{8 - 1} = \frac{100}{7} \approx 14.3\ &\text{Calculate the approximate } y\text{-intercept } b \approx 48 - 14.3(1) = 33.7\ &\text{Compare with the given options for the function:}\ &\quad \bullet \quad 10x + 35\ &\quad \bullet \quad 20x + 40\ &\quad \bullet \quad 2x + 40\ &\quad \bullet \quad 13x + 32\ &\text{The function } 13x + 32 \text{ has the closest slope (13) and y-intercept (32).}\ &\text{Verify fit: } 13(1)+32 = 45,\ 13(8)+32 = 136 \text{ (very close to the plotted points).} \end{aligned} $$ ## Predict the production for the 10th year $$ \begin{aligned} &\text{Using the chosen function: } f(x) = 13x + 32\ &\text{Substitute } x = 10 \text{ to predict the production in the 10th year:}\ &f(10) = 13(10) + 32 = 130 + 32 = 162 \end{aligned} $$ The data plot can be represented by the function $13x + 32$. Based on the scatter plot, we can predict that in the 10th year, the company will produce 162 engines. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Line of Best Fit Selection" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the line of best fit from the options

Predict the production for the 10th year

Answer: