what is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

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

Question

what is the equation of the line that is perpendicular to and has the same y-intercept as the given line?

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

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 of a Line", "Perpendicular Line Equations" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Perpendicular Line Equations" ] } ## Find the slope of the given line Using the *Slope of a Line* knowledge point $$ \begin{aligned} &(x_1, y_1) = (0, 1),\quad (x_2, y_2) = (5, 0)\ &m = \frac{0 - 1}{5 - 0} = -\frac{1}{5} \end{aligned} $$ ## Determine the perpendicular slope Using the *Perpendicular Line Equations* knowledge point $$ \begin{aligned} &m_{\perp} = -\frac{1}{m} = -\frac{1}{-\frac{1}{5}} = 5 \end{aligned} $$ ## Identify the y-intercept The given line passes through $(0, 1)$, so its $y$-intercept is $b = 1$. ## Write the perpendicular line equation Using the slope-intercept form $y = mx + b$ with $m = 5$ and $b = 1$: $$ y = 5x + 1 $$

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

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

(C) $y = 5x + 1$

(D) $y = 5x + 5$

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the perpendicular slope

Identify the y-intercept

Write the perpendicular line equation

Answer: