Question

1. the table represents some points on the graph of a linear function. write the function that represents this relationship.

\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline -4.5 & 26 \\\\ \\hline -2 & 18.5 \\\\ \\hline 3 & 3.5 \\\\ \\hline 7.5 & -10 \\\\ \\hline \\end{array}$$

Explanation:

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<reasoning>

Calculate the slope of the linear function

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18.5 - 26}{-2 - (-4.5)} = \frac{-7.5}{2.5} = -3
\]

Determine the y-intercept using a point

\[

$$\begin{aligned} y &= mx + b \\ 26 &= -3(-4.5) + b \\ 26 &= 13.5 + b \\ b &= 12.5 \end{aligned}$$

\]

Write the final linear equation

\[
y = -3x + 12.5
\]
</reasoning>

<answer>
\(y = -3x + 12.5\)
</answer>

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Answer:

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<reasoning>

Calculate the slope of the linear function

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18.5 - 26}{-2 - (-4.5)} = \frac{-7.5}{2.5} = -3
\]

Determine the y-intercept using a point

\[

$$\begin{aligned} y &= mx + b \\ 26 &= -3(-4.5) + b \\ 26 &= 13.5 + b \\ b &= 12.5 \end{aligned}$$

\]

Write the final linear equation

\[
y = -3x + 12.5
\]
</reasoning>

<answer>
\(y = -3x + 12.5\)
</answer>

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