4. Consider Line L with defining equation 2 y - ²x + 1/ . = 6 A. Find two ordered pairs (x₁, y₁) and (x2, y₂) that lie on the graph of line L. Check your results with a partner: if you have results different from your partner, does that mean that your or their results are inaccurate? Discuss why or why not? B. Use your two points from part A to find two different equations for line L in point-slope form. C. Do both of your point-slope equations from part B rearrange to have the same slope- intercept form? Why or why not? Can you provide reasoning to support your answer without having to perform the precise algebraic manipulations to verify explicitly?
4. Consider Line L with defining equation 2 y - ²x + 1/ . = 6 A. Find two ordered pairs (x₁, y₁) and (x2, y₂) that lie on the graph of line L. Check your results with a partner: if you have results different from your partner, does that mean that your or their results are inaccurate? Discuss why or why not? B. Use your two points from part A to find two different equations for line L in point-slope form. C. Do both of your point-slope equations from part B rearrange to have the same slope- intercept form? Why or why not? Can you provide reasoning to support your answer without having to perform the precise algebraic manipulations to verify explicitly?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Exploring Line Equations
**4. Consider Line \( \mathcal{L} \) with the defining equation:**
\[ y = -\frac{2}{3}x + \frac{1}{6}. \]
**A. Task:**
- Find two ordered pairs \((x_1, y_1)\) and \((x_2, y_2)\) that lie on the graph of line \( \mathcal{L} \).
- Check your results with a partner. If your results differ, consider if this indicates inaccuracy in either result. Discuss reasons for any discrepancies.
**B. Task:**
- Use your two points from part A to find two different equations for line \( \mathcal{L} \) in point-slope form.
**C. Inquiry:**
- Do both of your point-slope equations from part B rearrange to yield the same slope-intercept form? Why or why not?
- Provide reasoning to support your answer without performing detailed algebraic manipulations to verify explicitly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8612948-bcdc-496b-a0d4-ef3f637bada0%2F92b2e0ea-b39f-4ec8-a88f-995c30e9236d%2Fun2t0i7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Exploring Line Equations
**4. Consider Line \( \mathcal{L} \) with the defining equation:**
\[ y = -\frac{2}{3}x + \frac{1}{6}. \]
**A. Task:**
- Find two ordered pairs \((x_1, y_1)\) and \((x_2, y_2)\) that lie on the graph of line \( \mathcal{L} \).
- Check your results with a partner. If your results differ, consider if this indicates inaccuracy in either result. Discuss reasons for any discrepancies.
**B. Task:**
- Use your two points from part A to find two different equations for line \( \mathcal{L} \) in point-slope form.
**C. Inquiry:**
- Do both of your point-slope equations from part B rearrange to yield the same slope-intercept form? Why or why not?
- Provide reasoning to support your answer without performing detailed algebraic manipulations to verify explicitly.
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