7. $y = -\frac{3}{4}x$
8. $y = -2x + 5$
9. $x - y = 8$
10. $y + 2 = \frac{1}{2}x$
11. $3x + y = -5$
12. $3x + 2y = 6$

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Accepted Answer

{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Formula Rearrangement" ], "new_concepts": [ "Standard Form to Slope-Intercept Form" ], "current_concepts": [ "Slope-Intercept Form", "Formula Rearrangement", "Graphing Linear Equations" ] } ## Rewrite each equation in slope-intercept form $y = mx + b$ $$ \begin{aligned} \text{7.} \quad & y = -\frac{3}{4}x \ \text{8.} \quad & y = -2x + 5 \ \text{9.} \quad & y = x - 8 \ \text{10.} \quad & y = \frac{1}{2}x - 2 \ \text{11.} \quad & y = -3x - 5 \ \text{12.} \quad & y = -\frac{3}{2}x + 3 \end{aligned} $$ ## Identify the slope $m$ and y-intercept $(0, b)$ for each line $$ \begin{aligned} \text{7.} \quad & m = -\frac{3}{4}, \quad b = 0 \ \text{8.} \quad & m = -2, \quad b = 5 \ \text{9.} \quad & m = 1, \quad b = -8 \ \text{10.} \quad & m = \frac{1}{2}, \quad b = -2 \ \text{11.} \quad & m = -3, \quad b = -5 \ \text{12.} \quad & m = -\frac{3}{2}, \quad b = 3 \end{aligned} $$ ## Determine key plotting points for graphing $$ \begin{aligned} \text{7.} \quad & (0,0), \quad (4,-3) \ \text{8.} \quad & (0,5), \quad (1,3) \ \text{9.} \quad & (0,-8), \quad (8,0) \ \text{10.} \quad & (0,-2), \quad (4,0) \ \text{11.} \quad & (0,-5), \quad (-1,-2) \ \text{12.} \quad & (0,3), \quad (2,0) \end{aligned} $$ | No. | Equation | Slope-Intercept Form | Slope ($m$) | y-intercept ($b$) | |---|---|---|---|---| | 7 | $y = -\frac{3}{4}x$ | $y = -\frac{3}{4}x$ | $-\frac{3}{4}$ | $0$ | | 8 | $y = -2x + 5$ | $y = -2x + 5$ | $-2$ | $5$ | | 9 | $x - y = 8$ | $y = x - 8$ | $1$ | $-8$ | | 10 | $y + 2 = \frac{1}{2}x$ | $y = \frac{1}{2}x - 2$ | $\frac{1}{2}$ | $-2$ | | 11 | $3x + y = -5$ | $y = -3x - 5$ | $-3$ | $-5$ | | 12 | $3x + 2y = 6$ | $y = -\frac{3}{2}x + 3$ | $-\frac{3}{2}$ | $3$ | { "elements": [ { "type": "functiongraph", "params": [{"js": "-0.75*x", "latex": "y = -\frac{3}{4}x"}, -10, 10], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "7", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-2*x + 5", "latex": "y = -2x + 5"}, -10, 10], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "8", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "x - 8", "latex": "y = x - 8"}, -10, 10], "properties": { "strokeColor": "#55DDF2", "strokeWidth": 2, "name": "9", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "0.5*x - 2", "latex": "y = \frac{1}{2}x - 2"}, -10, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "name": "10", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-3*x - 5", "latex": "y = -3x - 5"}, -10, 10], "properties": { "strokeColor": "#F28A55", "strokeWidth": 2, "name": "11", "withLabel": true } }, { "type": "functiongraph", "params": [{"js": "-1.5*x + 3", "latex": "y = -\frac{3}{2}x + 3"}, -10, 10], "properties": { "strokeColor": "#F2C255", "strokeWidth": 2, "name": "12", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

No.	Equation	Slope-Intercept Form	Slope (\(m\))	y-intercept (\(b\))
8	\(y = -2x + 5\)	\(y = -2x + 5\)	\(-2\)	\(5\)
9	\(x - y = 8\)	\(y = x - 8\)	\(1\)	\(-8\)
10	\(y + 2 = \frac{1}{2}x\)	\(y = \frac{1}{2}x - 2\)	\(\frac{1}{2}\)	\(-2\)
11	\(3x + y = -5\)	\(y = -3x - 5\)	\(-3\)	\(-5\)
12	\(3x + 2y = 6\)	\(y = -\frac{3}{2}x + 3\)	\(-\frac{3}{2}\)	\(3\)

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Question

Explanation:

Rewrite each equation in slope-intercept form \(y = mx + b\)

Identify the slope \(m\) and y-intercept \((0, b)\) for each line

Determine key plotting points for graphing

Answer: