24. challenge: a line through the points $(2, 8)$ and $(-2, k)$ has a slope of $\frac{3}{4}$. what is the value of $k$?

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula", "Linear Equations Solving" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Linear Equations Solving" ] } ## Set up the slope equation $$ m = \frac{y_2 - y_1}{x_2 - x_1} \implies \frac{3}{4} = \frac{k - 8}{-2 - 2} $$ ## Simplify the denominator $$ \frac{3}{4} = \frac{k - 8}{-4} $$ ## Solve for k $$ \begin{aligned} 3 \cdot (-4) &= 4 \cdot (k - 8) \ -12 &= 4k - 32 \ 20 &= 4k \ k &= 5 \end{aligned} $$ $k = 5$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Slope Formula" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the slope equation

Simplify the denominator

Solve for k

Answer: