/*! 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 34 Find an equation of the line: w... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 34

Find an equation of the line: with \(y\) -intercept \((0,7)\) and slope \(\frac{4}{3}.\)

Short Answer

Expert verified
The equation of the line is \(y = \frac{4}{3}x + 7\).

Step by step solution

01

Identify the slope and y-intercept

The slope provides the rate at which the line increases or decreases, given as \(\frac{4}{3}\). The y-intercept is the point where the line crosses the y-axis, given as \((0, 7)\).
02

Use the slope-intercept form

The slope-intercept form of a line's equation is \(\boxed{y = mx + b}\), where \(m\) represents the slope, and \(b\) represents the y-intercept.
03

Substitute the values into the slope-intercept form

Substitute the slope \(\frac{4}{3}\) for \(m\), and the y-intercept value \(7\) for \(b\): \(y = \frac{4}{3}x + 7\). This gives the equation of the 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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear Equations
Linear equations are mathematical expressions that represent straight lines on a graph. They have variables to the first power, and they reveal relationships between these variables. The general form of a linear equation is \(Ax + By = C\), where \(A\), \(B\), and \(C\) are constants. Another common form is the slope-intercept form: \(y = mx + b\). This is useful because it directly gives you the slope and the y-intercept of the line. You can use linear equations to solve real-world problems, like calculating distances, predicting outcomes, and analyzing trends.
Slope
The slope of a line measures how steep it is. It is usually denoted by \(m\) in the slope-intercept form \(y = mx + b\). The slope represents the rate of change of \(y\) with respect to \(x\). If you have a slope \(\frac{4}{3}\), this means that for every 3 units you move to the right along the x-axis, you move 4 units up along the y-axis. A positive slope means the line rises as it moves from left to right; a negative slope means it falls. Zero slope means the line is horizontal, and an undefined slope means the line is vertical.
Y-intercept
The y-intercept of a line is where it crosses the y-axis on a graph. In the slope-intercept form \(y = mx + b\), the y-intercept is given by \(b\). This value tells you the point at which the line meets the y-axis, where \(x = 0\). For example, a y-intercept of 7 means the line crosses the y-axis at the point \((0, 7)\). Knowing the y-intercept helps you quickly sketch the line, as it's a key starting point for drawing or understanding the line's behavior.

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

Determine the domain of each function. $$f(x)=\sqrt{5 x+4}$$

The surface area of a person whose mass is 75 kg can be approximated by the function \(f(h)=0.144 h^{1 / 2}.\) where \(f(h)\) is measured in square meters and \(h\) is the person's height in centimeters. (Source: U.S. Oncology.) a) Find the approximate surface area of a person whose mass is 75 kg and whose height is 180cm. b) Find the approximate surface area of a person whose mass is 75 kg and whose height is 170cm. c) Graph the function \(f\) for \(0 \leq h \leq 200.\)

Find the domain of each function given below. $$g(x)=4 x^{3}+5 x^{2}-2 x$$

Find the domain of each function given below. $$g(x)=\sqrt{2-3 x}$$

It is theorized that the price per share of a stock is inversely proportional to the prime (interest) rate. In January 2010 , the price per share 5 of Apple Inc. stock was \(\$ 205.93\) and the prime rate \(R\) was \(3.25 \%\). The prime rate rose to \(4.75 \%\) in March 2010. (Source: finance, yahoo.com and Federal Reserve Board.) What was the price per share in March 2010 if the assumption of inverse proportionality is correct?
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.