/*! 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 76 Write equations of the lines thr... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 76

Write equations of the lines through the given point (a) parallel to and (b) perpendicular to the given line. $$5 x+3 y=0, \quad\left(\frac{7}{8}, \frac{3}{4}\right)$$

Short Answer

Expert verified
The equation of the line parallel to the given line is \(y=-\frac{5}{3}x+\frac{49}{24}\), and the equation of the line perpendicular to the given line is \(y=\frac{3}{5}x+\frac{9}{40}\).

Step by step solution

01

Find the slope of the given line

First, we need to put the equation into slope-intercept form, \(y=mx+b\), where \(m\) is the slope. Here, the equation is \(5x+3y=0\). Rearranging this, we get \(y=-\frac{5}{3}x\). So the slope of the given line is \(-\frac{5}{3}\).
02

Write the equation of the line parallel to the given line

Since parallel lines have the same slope, the equation of the line parallel to the given line that passes through the given point \(\left(\frac{7}{8},\frac{3}{4}\right)\) will use the same slope. Using the slope-intercept form, we can plug in \(m=-\frac{5}{3}\) and substitute the point as \(x_1, y_1\) in the formula \(y-y_1=m(x-x_1)\) to get the equation of this line.
03

Write the equation of the line perpendicular to the given line

As the slope of perpendicular lines are negative reciprocals of each other, the slope of the line perpendicular to the given line would be \(-1/(-\frac{5}{3}) = \frac{3}{5}\). Similar to the previous step, this slope is substituted into the point-slope form of a line equation, along with the given point, to obtain the equation of this line.

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

If \(f\) is an even function, determine whether \(g\) is even, odd, or neither. Explain. (a) \(g(x)=-f(x)\) (b) \(g(x)=f(-x)\) (c) \(g(x)=f(x)-2\) (d) \(g(x)=f(x-2)\)

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

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) Use the fact that 13 inches is approximately the same length as 33 centimeters to find a mathematical model that relates centimeters \(y\) to inches \(x\). Then use the model to find the numbers of centimeters in 10 inches and 20 inches.

A company produces a product for which the variable cost is 12.30 dollars per unit and the fixed costs are 98,000 dollars. The product sells for 17.98 dollars. Let \(x\) be the number of units produced and sold. (a) The total cost for a business is the sum of the variable cost and the fixed costs. Write the total cost \(C\) as a function of the number of units produced. (b) Write the revenue \(R\) as a function of the number of units sold. (c) Write the profit \(P\) as a function of the number of units sold. (Note: \(P=R-C\) ).

For groups of 80 or more people, a charter bus company determines the rate per person according to the formula Rate \(=8-0.05(n-80), \quad n \geq 80\) where the rate is given in dollars and \(n\) is the number of people. (a) Write the revenue \(R\) for the bus company as a function of \(n\) (b) Use the function in part (a) to complete the table. What can you conclude? $$\begin{array}{|l|l|l|l|l|l|l|l|}\hline n & 90 & 100 & 110 & 120 & 130 & 140 & 150 \\\\\hline R(n) & & & & & & & \\\\\hline\end{array}$$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics 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.