use your knowledge of x- and y-intercepts to choose the correct graph of the equation
\5x - 2y = 10\
enter the appropriate letter for the graph.

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Intercept Method", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Intercept Method", "Graphing Linear Equations" ] } ## Find the x-intercept Using the *Intercept Method* knowledge point $$ \begin{aligned} &y = 0 \ &5x - 2(0) = 10 \ &5x = 10 \ &x = 2 \implies (2, 0) \end{aligned} $$ ## Find the y-intercept Using the *Intercept Method* knowledge point $$ \begin{aligned} &x = 0 \ &5(0) - 2y = 10 \ &-2y = 10 \ &y = -5 \implies (0, -5) \end{aligned} $$ ## Match intercepts with the correct graph Using the *Graphing Linear Equations* knowledge point $$ \begin{aligned} &\text{Graph a: } x\text{-intercept } \approx 2, y\text{-intercept } \approx 5 \quad (\text{Incorrect}) \ &\text{Graph b: } x\text{-intercept } = 2, y\text{-intercept } = -5 \quad (\text{Correct}) \ &\text{Graph c: } x\text{-intercept } \approx -2, y\text{-intercept } \approx -5 \quad (\text{Incorrect}) \ &\text{Graph d: } x\text{-intercept } \approx -2, y\text{-intercept } \approx 5 \quad (\text{Incorrect}) \end{aligned} $$

a

b

c

d

{ "elements": [ { "type": "functiongraph", "params": [ { "js": "2.5*x - 5", "latex": "y = \frac{5}{2}x - 5" }, -2, 6 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3, "name": "5x - 2y = 10", "withLabel": true } }, { "type": "point", "params": [[2, 0]], "properties": { "name": "(2, 0)", "size": 4, "color": "#F2557F", "withLabel": true } }, { "type": "point", "params": [[0, -5]], "properties": { "name": "(0, -5)", "size": 4, "color": "#F2557F", "withLabel": true } } ], "timestamps": [0.5, 1.0] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Find the x-intercept

Find the y-intercept

Match intercepts with the correct graph

Answer: