Question

activity - finding greater slope

value: 1

which function has greater slope?

a. \\(3x + 4y = 5\\)
b. \\(y = 9x - 9\\)
c. \\(y - 5 = 0\\)
d. \\(4y = 8x - 4\\)

Explanation:

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<reasoning>

Convert equations to slope-intercept form

\[

$$\begin{aligned} &\text{a. } 3x + 4y = 5 \implies 4y = -3x + 5 \implies y = -\frac{3}{4}x + \frac{5}{4} \implies m = -\frac{3}{4}\\ &\text{b. } y = 9x - 9 \implies m = 9\\ &\text{c. } y - 5 = 0 \implies y = 5 \implies m = 0\\ &\text{d. } 4y = 8x - 4 \implies y = 2x - 1 \implies m = 2 \end{aligned}$$

\]

Compare the slopes

\[

$$\begin{aligned} &m_a = -0.75\\ &m_b = 9\\ &m_c = 0\\ &m_d = 2\\ &9 > 2 > 0 > -0.75 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>a. \(3x + 4y = 5\)</mcq-option>
<mcq-correct>b. \(y = 9x - 9\)</mcq-correct>
<mcq-option>c. \(y - 5 = 0\)</mcq-option>
<mcq-option>d. \(4y = 8x - 4\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert equations to slope-intercept form

\[

$$\begin{aligned} &\text{a. } 3x + 4y = 5 \implies 4y = -3x + 5 \implies y = -\frac{3}{4}x + \frac{5}{4} \implies m = -\frac{3}{4}\\ &\text{b. } y = 9x - 9 \implies m = 9\\ &\text{c. } y - 5 = 0 \implies y = 5 \implies m = 0\\ &\text{d. } 4y = 8x - 4 \implies y = 2x - 1 \implies m = 2 \end{aligned}$$

\]

Compare the slopes

\[

$$\begin{aligned} &m_a = -0.75\\ &m_b = 9\\ &m_c = 0\\ &m_d = 2\\ &9 > 2 > 0 > -0.75 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>a. \(3x + 4y = 5\)</mcq-option>
<mcq-correct>b. \(y = 9x - 9\)</mcq-correct>
<mcq-option>c. \(y - 5 = 0\)</mcq-option>
<mcq-option>d. \(4y = 8x - 4\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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