Question

determine which function has the greatest slope.

a) \\(y + 3 = -3(x - 5)\\) and b)

\\(\

$$\begin{array}{|c|c|} \\hline x & y \\\\ \\hline 1 & 5 \\\\ \\hline 2 & 9 \\\\ \\hline 3 & 13 \\\\ \\hline 4 & 17 \\\\ \\hline \\end{array}$$

\\)

solution

express the first equation in the slope-intercept form.

\\(y + 3 = -3(x - 5)\\)

\\(y + 3 = -3x + 15\\)

\\(y = -3x + 15 - 3\\)

\\(y = -3x + 12\\)

value: 1

find the slope of the first function.

a. 3
b. -3
c. 12
d. -12

Explanation:

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<reasoning>

Identify the first function and its equation

The first function is given by the equation:
\[y + 3 = -3(x - 5)\]

Convert the equation to slope-intercept form

\[

$$\begin{aligned} y + 3 &= -3x + 15\\ y &= -3x + 15 - 3\\ y &= -3x + 12 \end{aligned}$$

\]

Determine the slope of the first function

The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) represents the slope.
Comparing \(y = -3x + 12\) to \(y = mx + b\):
\[m = -3\]
</reasoning>

<answer>
<mcq-option>a. 3</mcq-option>
<mcq-correct>b. -3</mcq-correct>
<mcq-option>c. 12</mcq-option>
<mcq-option>d. -12</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the first function and its equation

The first function is given by the equation:
\[y + 3 = -3(x - 5)\]

Convert the equation to slope-intercept form

\[

$$\begin{aligned} y + 3 &= -3x + 15\\ y &= -3x + 15 - 3\\ y &= -3x + 12 \end{aligned}$$

\]

Determine the slope of the first function

The slope-intercept form of a linear equation is \(y = mx + b\), where \(m\) represents the slope.
Comparing \(y = -3x + 12\) to \(y = mx + b\):
\[m = -3\]
</reasoning>

<answer>
<mcq-option>a. 3</mcq-option>
<mcq-correct>b. -3</mcq-correct>
<mcq-option>c. 12</mcq-option>
<mcq-option>d. -12</mcq-option>
</answer>

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