/*! 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 48 Write each English sentence as a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 48

Write each English sentence as an equation in two variables. Then graph the equation. The \(y\) -value is the difference between four and twice the \(x\) -value.

Short Answer

Expert verified
The equivalent mathematical equation is \(y = 4 - 2x\) or \(y = -2x + 4\), depending on preferred format. The graph would be a straight line with y-intercept at 4 and slope of -2.

Step by step solution

01

Formulate the equation

The sentence 'The \(y\) -value is the difference between four and twice the \(x\) -value' can be translated into the equation \(y = 4 - 2x\). This is because 'the difference between four and twice the \(x\) -value' refers to subtracting two times the \(x\) -value from four.
02

Rearrange the equation (Optional)

This step is optional, depending on how one finds it easier to graph the equation. Some prefer the format \(y = mx + c\), which clearly shows the slope \(m\) and the y-intercept \(c\). The equation can be rearranged to this format, i.e., \(y = -2x + 4\).
03

Graph the equation

To graph the equation \(y = -2x + 4\), start by plotting the y-intercept (when \(x = 0, y = 4\)), then use the slope to find other points. Since the slope is -2, for each increment of 1 in \(x\), \(y\) will decrease by 2. Plotting these points and joining them with a straight line will give the graph of the equation.

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

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\sqrt{x}$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}-10 x-6 y-30=0$$

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{\frac{1}{3}}(x-4)$$

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}-2 x+y^{2}-15=0$$

Solve for \(y: \quad x=\frac{5}{y}+4\)
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Pure 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.