Question

question 1 (1 point)
given the line \\(y = -6x + 5\\), what is the slope and the y-intercept?
\\(m = 5\\), y-intercept \\((0, -6)\\)
\\(m = 6\\), y-intercept \\((0, 5)\\)
\\(m = -6\\), y-intercept \\((0, 5)\\)
\\(m = -6\\), y-intercept \\((5, 0)\\)

question 2 (1 point)
what is the slope and a point on the line of \\(y - 10 = -4(x + 3)\\)?
slope = -4; point is \\((-10, 3)\\)
slope = -4; point is \\((10, 3)\\)
slope = -4; point is \\((-3, 10)\\)
slope = 4; point is \\((-3, 10)\\)

Explanation:

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<reasoning>

Identify slope and y-intercept from slope-intercept form

\[

$$\begin{aligned} &y = mx + b \\ &y = -6x + 5 \\ &m = -6 \\ &\text{y-intercept} = (0, 5) \end{aligned}$$

\]

Identify slope and point from point-slope form

\[

$$\begin{aligned} &y - y_1 = m(x - x_1) \\ &y - 10 = -4(x + 3) \implies y - 10 = -4(x - (-3)) \\ &m = -4 \\ &(x_1, y_1) = (-3, 10) \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) \(m = 5\), y-intercept \((0, -6)\)</mcq-option>
<mcq-option>(B) \(m = 6\), y-intercept \((0, 5)\)</mcq-option>
<mcq-correct>(C) \(m = -6\), y-intercept \((0, 5)\)</mcq-correct>
<mcq-option>(D) \(m = -6\), y-intercept \((5, 0)\)</mcq-option>

Question 2

<mcq-option>(A) slope = \(-4\); point is \((-10, 3)\)</mcq-option>
<mcq-option>(B) slope = \(-4\); point is \((10, 3)\)</mcq-option>
<mcq-correct>(C) slope = \(-4\); point is \((-3, 10)\)</mcq-correct>
<mcq-option>(D) slope = \(4\); point is \((-3, 10)\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify slope and y-intercept from slope-intercept form

\[

$$\begin{aligned} &y = mx + b \\ &y = -6x + 5 \\ &m = -6 \\ &\text{y-intercept} = (0, 5) \end{aligned}$$

\]

Identify slope and point from point-slope form

\[

$$\begin{aligned} &y - y_1 = m(x - x_1) \\ &y - 10 = -4(x + 3) \implies y - 10 = -4(x - (-3)) \\ &m = -4 \\ &(x_1, y_1) = (-3, 10) \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

<mcq-option>(A) \(m = 5\), y-intercept \((0, -6)\)</mcq-option>
<mcq-option>(B) \(m = 6\), y-intercept \((0, 5)\)</mcq-option>
<mcq-correct>(C) \(m = -6\), y-intercept \((0, 5)\)</mcq-correct>
<mcq-option>(D) \(m = -6\), y-intercept \((5, 0)\)</mcq-option>

Question 2

<mcq-option>(A) slope = \(-4\); point is \((-10, 3)\)</mcq-option>
<mcq-option>(B) slope = \(-4\); point is \((10, 3)\)</mcq-option>
<mcq-correct>(C) slope = \(-4\); point is \((-3, 10)\)</mcq-correct>
<mcq-option>(D) slope = \(4\); point is \((-3, 10)\)</mcq-option>
</answer>

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