find the slope of the line containing the given points. (if an answer is undefined, enter undefined.)

$p_1(7, -5)$, $p_2(1, 7)$

Question

find the slope of the line containing the given points. (if an answer is undefined, enter undefined.)

$p_1(7, -5)$, $p_2(1, 7)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Slope Definition", "Coordinate Differences" ], "new_concepts": [], "current_concepts": [ "Slope Definition", "Coordinate Differences" ] } ## Identify the coordinates of the given points $$ P_1(x_1, y_1) = (7, -5),\quad P_2(x_2, y_2) = (1, 7) $$ ## Calculate the coordinate differences $$ \begin{aligned} \Delta y &= y_2 - y_1 = 7 - (-5) = 12\ \Delta x &= x_2 - x_1 = 1 - 7 = -6 \end{aligned} $$ ## Compute the slope $$ m = \frac{\Delta y}{\Delta x} = \frac{12}{-6} = -2 $$ Find the slope of the line containing the given points. (If an answer is undefined, enter UNDEFINED.) $P_1(7, -5), P_2(1, 7)$ -2 { "elements": [ { "type": "point", "params": [[7, -5]], "properties": { "name": "P1(7, -5)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "point", "params": [[1, 7]], "properties": { "name": "P2(1, 7)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[7, -5], [1, 7]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2 } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Slope Definition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the coordinates of the given points

Calculate the coordinate differences

Compute the slope

Answer: