we found the point (2, 7). find four more points and use the table below to graph the line. (i plotted on the screen. select the submit button to grade your response.)

\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{array}

write your answer in the form of a number.

Question

we found the point (2, 7). find four more points and use the table below to graph the line. (i plotted on the screen. select the submit button to grade your response.)

\begin{array}{|c|c|}
\hline
x & y \\
\hline
-2 & \\
\hline
-1 & \\
\hline
0 & \\
\hline
1 & \\
\hline
2 & \\
\hline
\end{array}

write your answer in the form of a number.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Linear Functions", "Function Evaluation" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Function Evaluation", "Graphing Linear Equations" ] } ## Identify the linear function Using the **Linear Functions** and **Function Evaluation** knowledge points $$ \begin{aligned} &\text{Given point: } (2, 7)\ &\text{The table shows } x = 2 \text{ is a blank, but the prompt states we found } (2, 7).\ &\text{Thus, for } x = 2, \text{ the corresponding } y \text{ value is } 7.\ &\text{Let the linear equation be } y = mx + b.\ &\text{Since } (2, 7) \text{ is on the line, } 7 = 2m + b. \end{aligned} $$ ## Determine the slope and equation Using the **Linear Functions** knowledge point $$ \begin{aligned} &\text{Assuming a standard integer slope to find a consistent linear relationship:}\ &\text{If } m = 2 \text{ (a common slope for introductory graphing problems):}\ &7 = 2(2) + b \implies b = 3\ &\text{This gives the linear equation: } y = 2x + 3. \end{aligned} $$ ## Evaluate the function for each x-value Using the **Function Evaluation** knowledge point $$ \begin{aligned} &\text{For } x = -2: \quad y = 2(-2) + 3 = -1\ &\text{For } x = -1: \quad y = 2(-1) + 3 = 1\ &\text{For } x = 0: \quad y = 2(0) + 3 = 3\ &\text{For } x = 1: \quad y = 2(1) + 3 = 5\ &\text{For } x = 2: \quad y = 2(2) + 3 = 7 \quad (\text{matches the given point}) \end{aligned} $$ We found the point (2, 7). Find four more points and use the table below to graph the line. | $x$ | $y$ | | :---: | :---: | | $-2$ | -1 | | $-1$ | 1 | | $0$ | 3 | | $1$ | 5 | | $2$ | 7 | { "elements": [ { "type": "point", "params": [[-2, -1]], "properties": { "name": "(-2, -1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[-1, 1]], "properties": { "name": "(-1, 1)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[0, 3]], "properties": { "name": "(0, 3)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 5]], "properties": { "name": "(1, 5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[2, 7]], "properties": { "name": "(2, 7)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "2*x + 3", "latex": "2x + 3"}, -5, 5], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Functions" ] }

\(x\)	\(y\)
\(-1\)	<blank>1</blank>
\(0\)	<blank>3</blank>
\(1\)	<blank>5</blank>
\(2\)	<blank>7</blank>

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QUESTION IMAGE

Question

Explanation:

Identify the linear function

Determine the slope and equation

Evaluate the function for each x-value

Answer: