Question

question 12 (5 points)
select the equation of the graphed line above.
a) \\(y = 3x - 5\\)
b) \\(y = x - 5\\)
c) \\(y = x + 5\\)
d) \\(y = 3x + 5\\)

question 13 (5 points)
write \\(9x + 3y = 15\\) in slope-intercept form.
a) \\(3y + 9x = 15\\)
b) \\(y = -3x + 5\\)
c) \\(y = -3x + 15\\)
d) \\(y = 3x + 5\\)

Explanation:

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<reasoning>

Identify the y-intercept of the graphed line

Using the Graphing Linear Equations knowledge point
\[
\text{The line crosses the } y\text{-axis at } (0, -5). \text{ Thus, the } y\text{-intercept } b = -5.
\]

Calculate the slope of the graphed line

Using the Slope of a Line knowledge point
\[

$$\begin{aligned} &\text{Identify two points on the line: } (0, -5) \text{ and } (2, 1).\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-5)}{2 - 0} = \frac{6}{2} = 3. \end{aligned}$$

\]

Write the equation of the line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = 3x - 5 \end{aligned}$$

\]

Convert the equation in Question 13 to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &9x + 3y = 15\\ &3y = -9x + 15\\ &y = -3x + 5 \end{aligned}$$

\]
</reasoning>

<answer>

Question 12

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

Question 13

<mcq-option>(A) \(3y + 9x = 15\)</mcq-option>
<mcq-correct>(B) \(y = -3x + 5\)</mcq-correct>
<mcq-option>(C) \(y = -3x + 15\)</mcq-option>
<mcq-option>(D) \(y = 3x + 5\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the y-intercept of the graphed line

Using the Graphing Linear Equations knowledge point
\[
\text{The line crosses the } y\text{-axis at } (0, -5). \text{ Thus, the } y\text{-intercept } b = -5.
\]

Calculate the slope of the graphed line

Using the Slope of a Line knowledge point
\[

$$\begin{aligned} &\text{Identify two points on the line: } (0, -5) \text{ and } (2, 1).\\ &m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-5)}{2 - 0} = \frac{6}{2} = 3. \end{aligned}$$

\]

Write the equation of the line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b\\ &y = 3x - 5 \end{aligned}$$

\]

Convert the equation in Question 13 to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &9x + 3y = 15\\ &3y = -9x + 15\\ &y = -3x + 5 \end{aligned}$$

\]
</reasoning>

<answer>

Question 12

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

Question 13

<mcq-option>(A) \(3y + 9x = 15\)</mcq-option>
<mcq-correct>(B) \(y = -3x + 5\)</mcq-correct>
<mcq-option>(C) \(y = -3x + 15\)</mcq-option>
<mcq-option>(D) \(y = 3x + 5\)</mcq-option>
</answer>

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