/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 65 Determine whether the lines are ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 65

Determine whether the lines are parallel, perpendicular, or neither. $$\begin{aligned} &L_{1}: y=\frac{1}{3} x-2\\\ &L_{2}: y=\frac{1}{3} x+3 \end{aligned}$$

Short Answer

Expert verified
The lines \(L_{1}\) and \(L_{2}\) are parallel.

Step by step solution

01

Determine the slopes of the given lines

The given lines are \(L_{1}: y=\frac{1}{3} x-2\) and \(L_{2}: y=\frac{1}{3} x+3\). From these equations, it's obvious that the slope of both \(L_{1}\) and \(L_{2}\) is \(\frac{1}{3}\).
02

Compare the slopes

By comparing the two slopes, it's clear that both lines have the same slope (\(\frac{1}{3}\)).
03

Make a conclusion

Since both lines have the same slope, they are parallel. Therefore, the lines \(L_{1}\) and \(L_{2}\) are parallel.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sketch the graph of the function. $$h(x)=\left\\{\begin{array}{ll}4-x^{2}, & x<-2 \\\3+x, & -2 \leq x<0 \\\x^{2}+1, & x \geq 0\end{array}\right.$$

The height \(y\) (in feet) of a baseball thrown by a child is $$y=-\frac{1}{10} x^{2}+3 x+6$$ where \(x\) is the horizontal distance (in feet) from where the ball was thrown. Will the ball fly over the head of another child 30 feet away trying to catch the ball? (Assume that the child who is trying to catch the ball holds a baseball glove at a height of 5 feet.)

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(P\) varies directly as \(x\) and inversely as the square of \(y .\) \(\left(P=\frac{28}{3} \text { when } x=42 \text { and } y=9 .\right)\)

Sketch the graph of the function. $$g(x)=[[x-3]]$$

An oceanographer took readings of the water temperatures \(C\) (in degrees Celsius) at several depths \(d\) (in meters). The data collected are shown as ordered pairs \((d, C)\) (Spreadsheet at LarsonPrecalculus.com) $$\begin{aligned} &(1000,4.2) \quad(4000,1.2)\\\ &(2000,1.9) \quad(5000,0.9)\\\ &(3000,1.4) \end{aligned}$$ A.Sketch a scatter plot of the data. B. Does it appear that the data can be modeled by the inverse variation model \(C=k / d ?\) If so, find \(k\) for each pair of coordinates. C. Determine the mean value of \(k\) from part (b) to find the inverse variation model \(C=k / d\) D. Use a graphing utility to plot the data points and the inverse model from part (c). E. Use the model to approximate the depth at which the water temperature is \(3^{\circ} \mathrm{C}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.