/*! 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 6 Sketch the graphs of the equatio... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 6

Sketch the graphs of the equations. $$ y-x=-1 $$

Short Answer

Expert verified
The graph of the equation \(y = x - 1\) is a straight line with a slope of 1 and a y-intercept of -1. To sketch the graph, plot the y-intercept at the point (0, -1) and use the slope to draw the line by going up 1 unit for every 1 unit to the right. The line passes through the points (0, -1) and (1, 0).

Step by step solution

01

Rearrange the equation in slope-intercept form (y = mx + b)

Given the equation, \(y - x = -1\), we need to isolate y. Add x to both sides of the equation to obtain: \(y = x - 1\) Now, we have the equation in the form of y = mx + b, where m = 1 (the slope) and b = -1 (the y-intercept).
02

Identify the slope and y-intercept

In the equation \(y = x - 1\), the slope (m) is 1, and the y-intercept (b) is -1. The slope indicates that for every 1 unit increase in x, y will also increase by 1 unit. The y-intercept indicates that when x is 0, y will be -1.
03

Plot the y-intercept

Plot the y-intercept on the graph. The y-intercept is -1, so we place a point at the coordinate (0, -1).
04

Use the slope to draw the line

Starting from the y-intercept point (0, -1), use the slope to draw the line. The slope is 1, which means the line goes up one unit every time it goes to the right one unit. So, from the y-intercept, move 1 unit to the right and 1 unit up, placing a point at the coordinate (1, 0). Draw a straight line through these two points, and this will be the graph of the equation. The graph of the equation \(y = x - 1\) is a straight line that passes through the points (0, -1) and (1, 0), with a slope of 1.

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

\(2 x+3 x^{2}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{3-1}{8+6}\)

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{\left(\frac{2}{3}\right)}{5}\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{2}-x=1\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(x^{2}+x+1=0\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

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.