Open in App
Log In Start studying!

Select your language

Suggested languages for you:
Deutsch (DE)
Deutsch (UK)
Deutsch (US)

Americas

Europe

Chapter 11: Chapter 11

Problem 219

Next question

Show that the slope of the segment joining \((1,2)\) and \((2,6)\) is equal to the slope of the segment joining \((5,15)\) and \((10,35)\)

Short Answer

Expert verified
The slopes of the segments joining \((1,2)\) and \((2,6)\) and \((5,15)\) and \((10,35)\) are equal, as we calculated both slopes to be 4 using the slope formula \( slope = \frac{y_2-y_1}{x_2-x_1} \).
See the step by step solution

Step by step solution

Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Try Premium for free

Over 22 million students worldwide already upgrade their learning with Vaia!

TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Find the slope of the segment joining \((1,2)\) and \((2,6)\)

Using the slope formula, we substitute the values from the given coordinates: \( slope_1 = \frac{6-2}{2-1} \) Now, perform the subtraction in the numerator and denominator: \( slope_1 = \frac{4}{1} \) So, the slope of this segment is: \( slope_1 = 4 \)

Step 2: Find the slope of the segment joining \((5,15)\) and \((10,35)\)

Now, we will calculate the slope of the second segment using the given coordinates and the slope formula: \( slope_2 = \frac{35-15}{10-5} \) Subtract the coordinates in the numerator and denominator: \( slope_2 = \frac{20}{5} \) So, the slope of this segment is: \( slope_2 = 4 \)

Step 3: Compare the two slopes

Now that we have the slopes of both segments, we can compare them to determine if they are equal: \( slope_1 = slope_2 \) Since both slopes are equal to 4, the statement is true. The slopes of the segments joining \((1,2)\) and \((2,6)\) and \((5,15)\) and \((10,35)\) are equal.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Access millions of textbook solutions in one place

  • Access over 3 million high quality textbook solutions
  • Access our popular flashcard, quiz, mock-exam and notes features
  • Access our smart AI features to upgrade your learning
Get Vaia Premium now
Access millions of textbook solutions in one place

Most popular questions from this chapter

Chapter 11

Write the equation in slope-intercept form; specify the slope and the \(y\) -intercept of the line. Sketch the graph of the equation. $2 \mathrm{x}-3 \mathrm{y}=5$
Chapter 11

Show that the graphs of \(3 x-y=9\) and \(6 x-2 y+9=0\) are parallel lines.
Chapter 11

Find the point of intersection of the graphs of \(3 \mathrm{x}-\mathrm{y}=5\) and \(9 \mathrm{x}-3 \mathrm{y}=15\)
Chapter 11

The equation of the line through \((-1,2)\) and \((3,1)\).
Chapter 11

What is the equation of the line through the point \((3,5)\) whose slope is 2 ?
See all solutions

More chapters from the book ‘Algebra and Trigonometry’

See all chapters

Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

  • Flashcards & Quizzes
  • AI Study Assistant
  • Smart Note-Taking
  • Mock-Exams
  • Study Planner
Join over 22 million students in learning with our Vaia App
Create your free account now
Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Math

Statistics

Read Explanation
Math

Pure Maths

Read Explanation
Math

Calculus

Read Explanation
Math

Probability and Statistics

Read Explanation
Math

Decision Maths

Read Explanation
Math

Geometry

Read Explanation
View all explanations