guided example 1

write the equation of a line, passing through the point $(5, -2)$, perpendicular to line $p$.

the slope of line $p$

the slope of the line perpendicular to line $p$ is $m =$

therefore, the equation of the line perpendicular to line $p$ is:
$y -$ select $=$ select $(x -$ select\)

Question

guided example 1

write the equation of a line, passing through the point $(5, -2)$, perpendicular to line $p$.

the slope of line $p$

the slope of the line perpendicular to line $p$ is $m =$

therefore, the equation of the line perpendicular to line $p$ is:
$y -$ select $=$ select $(x -$ select\)

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula", "Perpendicular Slopes", "Equations of Lines" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Perpendicular Slopes", "Equations of Lines" ] } ## Calculate the slope of Line p $$ \begin{aligned} &(x_1, y_1) = (1, -1)\ &(x_2, y_2) = (2, 2)\ &m_p = \frac{2 - (-1)}{2 - 1} = \frac{3}{1} = 3 \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} &m \cdot m_p = -1\ &m \cdot 3 = -1\ &m = -\frac{1}{3} \end{aligned} $$ ## Write the point-slope equation $$ \begin{aligned} &(x_0, y_0) = (5, -2)\ &y - y_0 = m(x - x_0)\ &y - (-2) = -\frac{1}{3}(x - 5)\ &y + 2 = -\frac{1}{3}(x - 5) \end{aligned} $$ ## Question 1 The slope of Line p is 3. ## Question 2 The slope of the line perpendicular to Line p is m= $-\frac{1}{3}$. ## Question 3 Therefore, the equation of the line perpendicular to Line p is: $y + 2$ = $-\frac{1}{3}$ ( $x - 5$ ) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Equations of Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of Line p

Determine the perpendicular slope

Write the point-slope equation

Answer:

Question 1

Question 2

Question 3