in the following exercises, use the slope formula to find the slope of the line between each pair of points.
85. $(2, 5), (4, 0)$
86. $(3, 6), (8, 0)$
87. $(-3, 3), (4, -5)$
88. $(-2, 4), (3, -1)$
89. $(-1, -2), (2, 5)$
90. $(-2, -1), (6, 5)$
91. $(4, -5), (1, -2)$
92. $(3, -6), (2, -2)$

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Accepted Answer

{ "quality": "clear", "question_count": 8, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Slope Formula" ], "current_concepts": [ "Slope Formula", "Coordinate Geometry" ] } ## State the slope formula $$ m = \frac{y_2 - y_1}{x_2 - x_1} $$ ## Calculate slopes for questions 85 to 88 $$ \begin{aligned} \text{85. } & m = \frac{0 - 5}{4 - 2} = -\frac{5}{2} \ \text{86. } & m = \frac{0 - 6}{8 - 3} = -\frac{6}{5} \ \text{87. } & m = \frac{-5 - 3}{4 - (-3)} = -\frac{8}{7} \ \text{88. } & m = \frac{-1 - 4}{3 - (-2)} = \frac{-5}{5} = -1 \end{aligned} $$ ## Calculate slopes for questions 89 to 92 $$ \begin{aligned} \text{89. } & m = \frac{5 - (-2)}{2 - (-1)} = \frac{7}{3} \ \text{90. } & m = \frac{5 - (-1)}{6 - (-2)} = \frac{6}{8} = \frac{3}{4} \ \text{91. } & m = \frac{-2 - (-5)}{1 - 4} = \frac{3}{-3} = -1 \ \text{92. } & m = \frac{-2 - (-6)}{2 - 3} = \frac{4}{-1} = -4 \end{aligned} $$ | No. | Problem | Answer | |---|---|---| | 85 | $(2, 5), (4, 0)$ | $-\frac{5}{2}$ | | 86 | $(3, 6), (8, 0)$ | $-\frac{6}{5}$ | | 87 | $(-3, 3), (4, -5)$ | $-\frac{8}{7}$ | | 88 | $(-2, 4), (3, -1)$ | $-1$ | | 89 | $(-1, -2), (2, 5)$ | $\frac{7}{3}$ | | 90 | $(-2, -1), (6, 5)$ | $\frac{3}{4}$ | | 91 | $(4, -5), (1, -2)$ | $-1$ | | 92 | $(3, -6), (2, -2)$ | $-4$ | { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Geometry", "Slope Formula" ] }

No.	Problem	Answer
86	\((3, 6), (8, 0)\)	\(-\frac{6}{5}\)
87	\((-3, 3), (4, -5)\)	\(-\frac{8}{7}\)
88	\((-2, 4), (3, -1)\)	\(-1\)
89	\((-1, -2), (2, 5)\)	\(\frac{7}{3}\)
90	\((-2, -1), (6, 5)\)	\(\frac{3}{4}\)
91	\((4, -5), (1, -2)\)	\(-1\)
92	\((3, -6), (2, -2)\)	\(-4\)

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Question

Explanation:

State the slope formula

Calculate slopes for questions 85 to 88

Calculate slopes for questions 89 to 92

Answer: