question 8

find the equation of the line parallel to $y = \frac{1}{2}x + 2$ that passes through the point $(4, 5)$ in slope-intercept form.

* $y = \frac{1}{2}x - 3$
* $y = \frac{1}{2}x + 3$
* $y = 2x + 4$
* $y = 2x - 4$

Question

question 8

find the equation of the line parallel to $y = \frac{1}{2}x + 2$ that passes through the point $(4, 5)$ in slope-intercept form.

* $y = \frac{1}{2}x - 3$
* $y = \frac{1}{2}x + 3$
* $y = 2x + 4$
* $y = 2x - 4$

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": [ "Parallel Lines Slope", "Slope-Intercept Form Conversion" ], "new_concepts": [], "current_concepts": [ "Parallel Lines Slope", "Slope-Intercept Form Conversion", "Linear Equations" ] } ## Determine the slope of the parallel line Using the *Parallel Lines Slope* knowledge point $$ \begin{aligned} &y = \frac{1}{2}x + 2 \implies m_1 = \frac{1}{2}\ &\text{Parallel lines have equal slopes} \implies m_2 = m_1 = \frac{1}{2} \end{aligned} $$ ## Use point-slope form to find the equation Using the *Slope-Intercept Form Conversion* knowledge point $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - 5 = \frac{1}{2}(x - 4) \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form Conversion* knowledge point $$ \begin{aligned} &y - 5 = \frac{1}{2}x - 2\ &y = \frac{1}{2}x + 3 \end{aligned} $$

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

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

(C) $y = 2x + 4$

(D) $y = 2x - 4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Parallel Lines Slope" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the slope of the parallel line

Use point-slope form to find the equation

Convert to slope-intercept form

Answer: