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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Question
![**How can you say that the points (1, -5), (3, -2), (7, 4) are collinear?**
This question explores whether the three given points lie on a single straight line. To determine this, you can calculate the slopes between pairs of points. The points are collinear if the slopes between all pairs of points are equal.
1. **Calculate the slope between (1, -5) and (3, -2):**
\[
\text{Slope} = \frac{-2 - (-5)}{3 - 1} = \frac{3}{2}
\]
2. **Calculate the slope between (3, -2) and (7, 4):**
\[
\text{Slope} = \frac{4 - (-2)}{7 - 3} = \frac{6}{4} = \frac{3}{2}
\]
3. **Calculate the slope between (1, -5) and (7, 4):**
\[
\text{Slope} = \frac{4 - (-5)}{7 - 1} = \frac{9}{6} = \frac{3}{2}
\]
Since all slopes are equal, the points (1, -5), (3, -2), and (7, 4) are collinear.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc460cec6-7f94-4fbe-b608-c65e915f11c7%2Fd1a193db-ee51-42c5-99cd-5d4b4f8df16c%2F9qa7hr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**How can you say that the points (1, -5), (3, -2), (7, 4) are collinear?**
This question explores whether the three given points lie on a single straight line. To determine this, you can calculate the slopes between pairs of points. The points are collinear if the slopes between all pairs of points are equal.
1. **Calculate the slope between (1, -5) and (3, -2):**
\[
\text{Slope} = \frac{-2 - (-5)}{3 - 1} = \frac{3}{2}
\]
2. **Calculate the slope between (3, -2) and (7, 4):**
\[
\text{Slope} = \frac{4 - (-2)}{7 - 3} = \frac{6}{4} = \frac{3}{2}
\]
3. **Calculate the slope between (1, -5) and (7, 4):**
\[
\text{Slope} = \frac{4 - (-5)}{7 - 1} = \frac{9}{6} = \frac{3}{2}
\]
Since all slopes are equal, the points (1, -5), (3, -2), and (7, 4) are collinear.
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