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

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

$y = \frac{1}{3}x + \frac{5}{3}$

$y = \frac{1}{3}x - \frac{5}{3}$

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

Question

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

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

$y = \frac{1}{3}x + \frac{5}{3}$

$y = \frac{1}{3}x - \frac{5}{3}$

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

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": [ "Slope-Intercept Form", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Point-Slope Form" ] } ## Identify the given values Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &m = \frac{1}{3}\ &(x_1, y_1) = (-2, 1) \end{aligned} $$ ## Apply point-slope equation Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - 1 = \frac{1}{3}(x - (-2))\ &y - 1 = \frac{1}{3}(x + 2) \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y - 1 = \frac{1}{3}x + \frac{2}{3}\ &y = \frac{1}{3}x + \frac{2}{3} + 1\ &y = \frac{1}{3}x + \frac{5}{3} \end{aligned} $$

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

(B) $y = \frac{1}{3}x + \frac{5}{3}$

(C) $y = \frac{1}{3}x - \frac{5}{3}$

(D) $y = \frac{1}{3}x + 1$

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QUESTION IMAGE

Question

Explanation:

Identify the given values

Apply point-slope equation

Convert to slope-intercept form

Answer: