Question

which of the following is the graph of this function rule?
\\y = 3 - 2x\\

Explanation:

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<reasoning>

Identify the y-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &y = -2x + 3\\ &\text{For } x = 0:\\ &y = 3 - 2(0) = 3\\ &\text{The } y\text{-intercept is } (0, 3). \end{aligned}$$

\]

Calculate key ordered pairs

Using the Ordered Pairs and Coordinate Plane knowledge points
\[

$$\begin{aligned} &\text{For } x = 1:\\ &y = 3 - 2(1) = 1 \implies (1, 1)\\ &\text{For } x = 2:\\ &y = 3 - 2(2) = -1 \implies (2, -1) \end{aligned}$$

\]

Match points to the correct graph

Using the Coordinate Plane knowledge point
\[

$$\begin{aligned} &\text{Graph 1 (Left): Passes through } (0, 3), (1, 1), \text{ and } (2, -1).\\ &\text{Graph 2 (Middle): Passes through } (-2, 1), (-1, -1), \text{ and } (0, -3).\\ &\text{Graph 3 (Right): Passes through } (0, 3), (-1, 1), \text{ and } (-2, -1).\\ &\text{Therefore, the first graph is correct.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) The first graph (left), passing through (0, 3), (1, 1), and (2, -1)</mcq-correct>
<mcq-option>(B) The second graph (middle), passing through (-2, 1), (-1, -1), and (0, -3)</mcq-option>
<mcq-option>(C) The third graph (right), passing through (0, 3), (-1, 1), and (-2, -1)</mcq-option>
</answer>

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"properties": {
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Answer:

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<reasoning>

Identify the y-intercept

Using the Linear Equations knowledge point
\[

$$\begin{aligned} &y = -2x + 3\\ &\text{For } x = 0:\\ &y = 3 - 2(0) = 3\\ &\text{The } y\text{-intercept is } (0, 3). \end{aligned}$$

\]

Calculate key ordered pairs

Using the Ordered Pairs and Coordinate Plane knowledge points
\[

$$\begin{aligned} &\text{For } x = 1:\\ &y = 3 - 2(1) = 1 \implies (1, 1)\\ &\text{For } x = 2:\\ &y = 3 - 2(2) = -1 \implies (2, -1) \end{aligned}$$

\]

Match points to the correct graph

Using the Coordinate Plane knowledge point
\[

$$\begin{aligned} &\text{Graph 1 (Left): Passes through } (0, 3), (1, 1), \text{ and } (2, -1).\\ &\text{Graph 2 (Middle): Passes through } (-2, 1), (-1, -1), \text{ and } (0, -3).\\ &\text{Graph 3 (Right): Passes through } (0, 3), (-1, 1), \text{ and } (-2, -1).\\ &\text{Therefore, the first graph is correct.} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) The first graph (left), passing through (0, 3), (1, 1), and (2, -1)</mcq-correct>
<mcq-option>(B) The second graph (middle), passing through (-2, 1), (-1, -1), and (0, -3)</mcq-option>
<mcq-option>(C) The third graph (right), passing through (0, 3), (-1, 1), and (-2, -1)</mcq-option>
</answer>

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