/*! 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 8 Use the given conditions to writ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 8

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-4,2)\) and perpendicular to the line whose equation is \(y=\frac{1}{3} x+7\)

Short Answer

Expert verified
The point-slope form of the line is \(y - 2 = -3(x + 4)\), and the slope-intercept form is \(y = -3x - 10\).

Step by step solution

01

Find the slope of the new line

The slope of the line given by the equation \(y=\frac{1}{3}x+7\) is \(\frac{1}{3}\). A line is perpendicular to another if its slope is the negative reciprocal of the other line's slope. Therefore, the slope of the new line is \(-3\).
02

Write the equation of the line in point-slope form

The point-slope form of a line is given by: \(y - y_1 = m(x - x_1)\) where \(m\) is the slope and \((x_1,y_1)\) is a point on the line. Substituting \(-3\) for the slope and \((-4,2)\) for \((x_1,y_1)\), gives: \(y - 2 = -3(x + 4)\) which simplifies to: \(y = -3x - 10\).
03

Write the equation of the line in slope-intercept form

The slope-intercept form of a line is given by \(y = mx + b\) where \(m\) is the slope and \(b\) is the y-intercept. The y-intercept is the y-coordinate of the point where the line crosses the y-axis. From previous steps we know that the slope \(m\) of new line is \(-3\). Plugging this and the given point (-4,2) into the slope-intercept form, we can solve for \(b\): \(2 = -3(-4) + b\). Solving for \(b\) we get \(b = -10\). Thus, the slope-intercept form of the given line is \(y = -3x - 10\).

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

In Exercises \(105-108,\) you will be developing functions that model given conditions. A car was purchased for \(\$ 22,500\). The value of the car decreased by \(\$ 3200\) per year for the first six years. Write a function that describes the value of the car, \(V,\) after \(x\) years, where \(0 \leq x \leq 6 .\) Then find and interpret \(V(3)\)

How is the standard form of a circle's equation obtained from its general form?

complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$ x^{2}+y^{2}-x+2 y+1=0 $$

give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. $$ x^{2}+y^{2}=16 $$

Furry Finances A pet insurance policy has a monthly rate that is a function of the age of the insured dog or cat. For pets whose age does not exceed \(4,\) the monthly cost is \(\$ 20\). The cost then increases by \(\$ 2\) for each successive year of the pet's age. $$ \begin{array}{cc} \text { Age Not Exceeding } & \text { Monthly Cost } \\ \hline 4 & \$ 20 \\ 5 & \$ 22 \\ 6 & \$ 24 \end{array} $$ The cost schedule continues in this manner for ages not exceeding \(10 .\) The cost for pets whose ages exceed 10 is S40. Use this information to create a graph that shows the monthly cost of the insurance, \(f(x)\), for a pet of age \(x,\) where the function's domain is \([0,14]\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Statistics

Read Explanation

Probability and Statistics

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.