which function is most likely graphed on the coordinate plane below?

* (f(x) = 3x - 11)
* (f(x) = -4x + 12)
* (f(x) = 4x + 13)
* (f(x) = -5x - 19)

Question

which function is most likely graphed on the coordinate plane below?

* (f(x) = 3x - 11)
* (f(x) = -4x + 12)
* (f(x) = 4x + 13)
* (f(x) = -5x - 19)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Functions", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Linear Functions", "Slope-Intercept Form", "Graphical Analysis" ] } ## Analyze the slope and intercepts from the graph $$ \begin{aligned} &\text{Slope } (m) < 0 \quad (\text{line falls from left to right})\ &\text{y-intercept } (b) < 0 \quad (\text{line crosses the y-axis below the origin } (0,0))\ &\text{x-intercept } < 0 \quad (\text{line crosses the x-axis to the left of the origin } (0,0)) \end{aligned} $$ ## Evaluate the given options $$ \begin{aligned} &f(x) = 3x - 11 \implies m = 3 > 0 \quad (\text{Incorrect})\ &f(x) = -4x + 12 \implies b = 12 > 0 \quad (\text{Incorrect})\ &f(x) = 4x + 13 \implies m = 4 > 0 \quad (\text{Incorrect})\ &f(x) = -5x - 19 \implies m = -5 < 0, \ b = -19 < 0 \quad (\text{Correct}) \end{aligned} $$

(A) $f(x) = 3x - 11$

(B) $f(x) = -4x + 12$

(C) $f(x) = 4x + 13$

(D) $f(x) = -5x - 19$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the slope and intercepts from the graph

Evaluate the given options

Answer: