which equation represents the line that passes through points $(1, -5)$ and $(3, -17)$?

$y = -6x + 1$
$y = 6x + 1$
$y = -6x - 1$
$y = 6x - 1$

Question

which equation represents the line that passes through points $(1, -5)$ and $(3, -17)$?

$y = -6x + 1$
$y = 6x + 1$
$y = -6x - 1$
$y = 6x - 1$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Slope of a Line", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Point-Slope Form", "Parallel Line Equations" ] } ## Calculate the slope of the line Using the *Slope of a Line* knowledge point $$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-17 - (-5)}{3 - 1} = \frac{-12}{2} = -6 $$ ## Write the equation in point-slope form Using the *Point-Slope Form* knowledge point $$ \begin{aligned} y - y_1 &= m(x - x_1) \ y - (-5) &= -6(x - 1) \ y + 5 &= -6x + 6 \end{aligned} $$ ## Convert to slope-intercept form Using the *Point-Slope Form* knowledge point $$ \begin{aligned} y &= -6x + 6 - 5 \ y &= -6x + 1 \end{aligned} $$

(A) $y = -6x + 1$

(B) $y = 6x + 1$

(C) $y = -6x - 1$

(D) $y = 6x - 1$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Slope of a Line" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of the line

Write the equation in point-slope form

Convert to slope-intercept form

Answer: