exercises 13-5
in exercises 1-6, identify the slope and the y-intercept. express each slope as a fraction when appropriate.
1. $y = \frac{4}{5}x + 1$
2. $y = -x - 7$
3. $y = -8x + 2$
4. $4x + y = 9$
5. $x - y = 5$
6. $3x + 6y = 18$

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{ "quality": "clear", "question_count": 6, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Standard Form to Slope-Intercept Form", "y-intercept" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Standard Form to Slope-Intercept Form", "y-intercept", "Slope Formula" ] } ## Convert equations to slope-intercept form $y = mx + b$ $$ \begin{aligned} &\text{1. } y = \frac{4}{5}x + 1 \quad \text{(already in form)} \ &\text{2. } y = -x - 7 \quad \text{(already in form)} \ &\text{3. } y = -8x + 2 \quad \text{(already in form)} \ &\text{4. } 4x + y = 9 \implies y = -4x + 9 \ &\text{5. } x - y = 5 \implies y = x - 5 \ &\text{6. } 3x + 6y = 18 \implies 6y = -3x + 18 \implies y = -\frac{1}{2}x + 3 \end{aligned} $$ ## Identify slope $m$ and y-intercept $b$ for each equation $$ \begin{aligned} &\text{1. } m = \frac{4}{5}, \quad b = 1 \ &\text{2. } m = -1, \quad b = -7 \ &\text{3. } m = -8, \quad b = 2 \ &\text{4. } m = -4, \quad b = 9 \ &\text{5. } m = 1, \quad b = -5 \ &\text{6. } m = -\frac{1}{2}, \quad b = 3 \end{aligned} $$ | No. | Slope | y-intercept | |---|---|---| | 1 | $\frac{4}{5}$ | $1$ | | 2 | $-1$ | $-7$ | | 3 | $-8$ | $2$ | | 4 | $-4$ | $9$ | | 5 | $1$ | $-5$ | | 6 | $-\frac{1}{2}$ | $3$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

No.	Slope	y-intercept
2	\(-1\)	\(-7\)
3	\(-8\)	\(2\)
4	\(-4\)	\(9\)
5	\(1\)	\(-5\)
6	\(-\frac{1}{2}\)	\(3\)

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Question

Explanation:

Convert equations to slope-intercept form \(y = mx + b\)

Identify slope \(m\) and y-intercept \(b\) for each equation

Answer: