what is the equation of this linear function?

(y = ?x + \square)

Question

what is the equation of this linear function?

(y = ?x + \square)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Coordinate Plane", "Slope Calculation", "Slope-Intercept Form" ], "new_concepts": [], "current_concepts": [ "Coordinate Plane", "Slope Calculation", "Slope-Intercept Form", "Linear Function Modeling" ] } ## Identify the y-intercept from the graph Using the **Coordinate Plane** knowledge point $$ (x_1, y_1) = (0, -1) \implies b = -1 $$ ## Calculate the slope of the line Using the **Slope Calculation** knowledge point $$ \begin{aligned} &(x_1, y_1) = (0, -1),\quad (x_2, y_2) = (1, -5)\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - (-1)}{1 - 0} = -4 \end{aligned} $$ ## Write the linear equation Using the **Slope-Intercept Form** knowledge point $$ \begin{aligned} &y = mx + b\ &y = -4x - 1 \end{aligned} $$ What is the equation of this linear function? $y =$ $-4$$x +$ $-1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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Question

Explanation:

Identify the y-intercept from the graph

Calculate the slope of the line

Write the linear equation

Answer: