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\\)

Explanation:

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<reasoning>

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

\[

$$\begin{aligned} &-3x + 4y = 7 \implies 4y = 3x + 7 \implies y = \frac{3}{4}x + \frac{7}{4}\\ &m_1 = \frac{3}{4}\\ &m_2 = -\frac{1}{m_1} = -\frac{4}{3} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

<mcq-correct>(A) \(y = -3/5x + 2\)</mcq-correct>
<mcq-option>(B) \(y = -3/5x + 4\)</mcq-option>
<mcq-option>(C) \(y = 3/5x + 3\)</mcq-option>
<mcq-option>(D) \(y = -3/5x + 1\)</mcq-option>

Question 6

<mcq-correct>(A) \(y = x + 4\)</mcq-correct>
<mcq-option>(B) \(y = x - 4\)</mcq-option>
<mcq-option>(C) \(y = -x + 4\)</mcq-option>
<mcq-option>(D) \(y = -x - 4\)</mcq-option>

Question 7

<mcq-option>(A) \(3/4\)</mcq-option>
<mcq-correct>(B) \(-4/3\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

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

\[

$$\begin{aligned} &-3x + 4y = 7 \implies 4y = 3x + 7 \implies y = \frac{3}{4}x + \frac{7}{4}\\ &m_1 = \frac{3}{4}\\ &m_2 = -\frac{1}{m_1} = -\frac{4}{3} \end{aligned}$$

\]
</reasoning>

<answer>

Question 5

<mcq-correct>(A) \(y = -3/5x + 2\)</mcq-correct>
<mcq-option>(B) \(y = -3/5x + 4\)</mcq-option>
<mcq-option>(C) \(y = 3/5x + 3\)</mcq-option>
<mcq-option>(D) \(y = -3/5x + 1\)</mcq-option>

Question 6

<mcq-correct>(A) \(y = x + 4\)</mcq-correct>
<mcq-option>(B) \(y = x - 4\)</mcq-option>
<mcq-option>(C) \(y = -x + 4\)</mcq-option>
<mcq-option>(D) \(y = -x - 4\)</mcq-option>

Question 7

<mcq-option>(A) \(3/4\)</mcq-option>
<mcq-correct>(B) \(-4/3\)</mcq-correct>
</answer>

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