Question

linear relations - creating an equation

1. determine the equation for the following.

reading a book
chapters left in book vs number of evenings reading

1. determine the equation for the following.

\

$$\begin{tabular}{|c|c|} \\hline \\text{number of people} & \\text{cost of banquet} \\\\ \\hline 135 & \\$8,250 \\\\ \\hline 180 & \\$10,950 \\\\ \\hline 225 & \\$13,650 \\\\ \\hline 270 & \\$16,350 \\\\ \\hline \\end{tabular}$$

Explanation:

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<reasoning>

Find the slope and y-intercept for Question 9

\[

$$\begin{aligned} &\text{Points on the line: } (0, 16) \text{ and } (4, 6)\\ &m = \frac{6 - 16}{4 - 0} = \frac{-10}{4} = -2.5\\ &b = 16\\ &y = -2.5x + 16 \end{aligned}$$

\]

Find the slope and y-intercept for Question 10

\[

$$\begin{aligned} &\text{Points from the table: } (135, 8250) \text{ and } (180, 10950)\\ &m = \frac{10950 - 8250}{180 - 135} = \frac{2700}{45} = 60\\ &y - 8250 = 60(x - 135)\\ &y = 60x - 8100 + 8250\\ &y = 60x + 150 \end{aligned}$$

\]
</reasoning>

<answer>

Question 9

\(y = -2.5x + 16\) (where \(y\) represents the chapters left in the book and \(x\) represents the number of evenings reading)

Question 10

\(y = 60x + 150\) (where \(y\) represents the cost of the banquet and \(x\) represents the number of people)
</answer>

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"subject": "Mathematics",
"question_type": "Multi-part",
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"Mathematics",
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Answer:

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<reasoning>

Find the slope and y-intercept for Question 9

\[

$$\begin{aligned} &\text{Points on the line: } (0, 16) \text{ and } (4, 6)\\ &m = \frac{6 - 16}{4 - 0} = \frac{-10}{4} = -2.5\\ &b = 16\\ &y = -2.5x + 16 \end{aligned}$$

\]

Find the slope and y-intercept for Question 10

\[

$$\begin{aligned} &\text{Points from the table: } (135, 8250) \text{ and } (180, 10950)\\ &m = \frac{10950 - 8250}{180 - 135} = \frac{2700}{45} = 60\\ &y - 8250 = 60(x - 135)\\ &y = 60x - 8100 + 8250\\ &y = 60x + 150 \end{aligned}$$

\]
</reasoning>

<answer>

Question 9

\(y = -2.5x + 16\) (where \(y\) represents the chapters left in the book and \(x\) represents the number of evenings reading)

Question 10

\(y = 60x + 150\) (where \(y\) represents the cost of the banquet and \(x\) represents the number of people)
</answer>

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