graphing. first graph the equations, and then type the solution.

\y = \frac{3}{2}x + 5\

\y = 2x + 6\

click to select points on the graph.

Question

graphing. first graph the equations, and then type the solution.

\y = \frac{3}{2}x + 5\

\y = 2x + 6\

click to select points on the graph.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Systems of Equations", "Graphical Solutions", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Systems of Equations", "Graphical Solutions", "Graphing Linear Equations" ] } ## Equate the linear equations to find the intersection point $$ \begin{aligned} \frac{3}{2}x + 5 &= 2x + 6 \ 5 - 6 &= 2x - \frac{3}{2}x \ -1 &= \frac{1}{2}x \ x &= -2 \end{aligned} $$ ## Substitute the x-value back to find the y-value $$ \begin{aligned} y &= 2(-2) + 6 \ y &= -4 + 6 \ y &= 2 \end{aligned} $$ ## Determine key plotting points for both lines $$ \begin{aligned} &\text{Line 1: } y = \frac{3}{2}x + 5 \implies (0, 5), (-2, 2) \ &\text{Line 2: } y = 2x + 6 \implies (0, 6), (-2, 2) \end{aligned} $$ Solve the system of equations by graphing. First graph the equations, and then type the solution. $y = \frac{3}{2}x + 5$ $y = 2x + 6$ The solution to the system of equations is $(-2, 2)$. { "elements": [ { "type": "functiongraph", "params": [{"js": "1.5*x + 5", "latex": "y = \frac{3}{2}x + 5"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "y = 1.5x + 5", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "2*x + 6", "latex": "y = 2x + 6"}, -10, 10], "properties": { "strokeColor": "#5583F2", "strokeWidth": 3, "name": "y = 2x + 6", "withLabel": true } }, { "type": "point", "params": [[-2, 2]], "properties": { "name": "(-2, 2)", "size": 5, "strokeColor": "#F2557F", "fillColor": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Graphical Solutions" ] }

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QUESTION IMAGE

Question

Explanation:

Equate the linear equations to find the intersection point

Substitute the x-value back to find the y-value

Determine key plotting points for both lines

Answer: