which is the equation of a line that has a slope of $-\frac{2}{3}$ and passes through point $(-3, -1)$?

$y = -\frac{2}{3}x + 1$

$y = -\frac{2}{3}x + 3$

$y = -\frac{2}{3}x - 1$

$y = -\frac{2}{3}x - 3$

Question

which is the equation of a line that has a slope of $-\frac{2}{3}$ and passes through point $(-3, -1)$?

$y = -\frac{2}{3}x + 1$

$y = -\frac{2}{3}x + 3$

$y = -\frac{2}{3}x - 1$

$y = -\frac{2}{3}x - 3$

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-Intercept Form", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Point-Slope Form" ] } ## Identify given values Using the *Point-Slope Form* and *Slope-Intercept Form* knowledge points $$ \begin{aligned} &m = -\frac{2}{3}\ &(x_1, y_1) = (-3, -1) \end{aligned} $$ ## Apply point-slope formula Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - (-1) = -\frac{2}{3}(x - (-3))\ &y + 1 = -\frac{2}{3}(x + 3) \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y + 1 = -\frac{2}{3}x - 2\ &y = -\frac{2}{3}x - 3 \end{aligned} $$

(A) $y = -\frac{2}{3}x + 1$

(B) $y = -\frac{2}{3}x + 3$

(C) $y = -\frac{2}{3}x - 1$

(D) $y = -\frac{2}{3}x - 3$

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

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QUESTION IMAGE

Question

Explanation:

Identify given values

Apply point-slope formula

Convert to slope-intercept form

Answer: