find the equation of a line parallel to $y = -3/5x + 2$ and passing through...

question 6 (1 point)
write the equation of a line passing through $(3,7)$ and $(-5, -1)$.
$\bigcirc y = x + 4$
$\bigcirc y = x - 4$
$\bigcirc y = -x + 4$
$\bigcirc y = -x - 4$

question 7 (1 point)
find the slope of a line perpendicular to the line $-3x + 4y = 7$.
$\bigcirc -4/3$
$\bigcirc 3/4$

Question

find the equation of a line parallel to $y = -3/5x + 2$ and passing through...

question 6 (1 point)
write the equation of a line passing through $(3,7)$ and $(-5, -1)$.
$\bigcirc y = x + 4$
$\bigcirc y = x - 4$
$\bigcirc y = -x + 4$
$\bigcirc y = -x - 4$

question 7 (1 point)
find the slope of a line perpendicular to the line $-3x + 4y = 7$.
$\bigcirc -4/3$
$\bigcirc 3/4$

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Point-Slope Form" ], "new_concepts": [ "Parallel Lines", "Perpendicular Lines" ], "current_concepts": [ "Slope-Intercept Form", "Point-Slope Form", "Parallel Lines", "Perpendicular Lines" ] } ## Find the parallel line equation $$ \begin{aligned} &y = -\frac{3}{5}x + 2 \implies m = -\frac{3}{5}\ &\text{Passing through } (5, -1):\ &y - (-1) = -\frac{3}{5}(x - 5)\ &y + 1 = -\frac{3}{5}x + 3\ &y = -\frac{3}{5}x + 2 \end{aligned} $$ ## Find the equation through two points $$ \begin{aligned} &m = \frac{-1 - 7}{-5 - 3} = \frac{-8}{-8} = 1\ &y - 7 = 1(x - 3)\ &y = x + 4 \end{aligned} $$ ## Find the perpendicular slope $$ \begin{aligned} &-3x + 4y = 7 \implies 4y = 3x + 7 \implies y = \frac{3}{4}x + \frac{7}{4}\ &m_1 = \frac{3}{4}\ &m_2 = -\frac{1}{m_1} = -\frac{4}{3} \end{aligned} $$ ## Question 5 (A) $y = -3/5x + 2$

(B) $y = -3/5x + 4$

(C) $y = 3/5x + 3$

(D) $y = -3/5x + 1$ ## Question 6 (A) $y = x + 4$

(B) $y = x - 4$

(C) $y = -x + 4$

(D) $y = -x - 4$ ## Question 7 (A) $3/4$

(B) $-4/3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the parallel line equation

Find the equation through two points

Find the perpendicular slope

Answer:

Question 5

Question 6

Question 7