/*! 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 1 Graph. (Unless directed otherwis... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 1

Graph. (Unless directed otherwise, assume that "Graph" means "Graph by hand.") $$y=x+4$$

Short Answer

Expert verified
Identify the y-intercept \((0, 4)\), find another point using the slope \((1, 5)\), plot these points, and draw a line through them.

Step by step solution

01

Identify the equation form

The given equation is in the form of a linear equation, which is generally written as \[ y = mx + b \]. Here, \[ m = 1 \] (slope) and \[ b = 4 \] (y-intercept).
02

Determine the y-intercept

The y-intercept is the point where the line crosses the y-axis, which happens when \[ x = 0 \]. For the given equation \[ y = x + 4 \], substituting \[ x = 0 \] gives \[ y = 4 \]. Thus, the y-intercept is \((0, 4)\).
03

Determine another point using the slope

The slope \[ m \] is the change in \[ y \] for a one-unit change in \[ x \]. Since \[ m = 1 \], for every \[ x \] increase by 1, \[ y \] also increases by 1. Starting from \((0,4)\), if \[ x \] increases by 1, \[ y \] becomes \[ 4+1 = 5 \]. Therefore, another point is \((1, 5)\).
04

Plot the points on a coordinate system

On graph paper, plot the points identified: \((0, 4)\) and \((1, 5)\).
05

Draw the line

Using a ruler, draw a straight line through the points \((0, 4)\) and \((1, 5)\). Extend this line in both directions.
06

Label the graph

Label the y-intercept \((0, 4)\), the other point \((1, 5)\), and the equation of the line \( y = x + 4 \) on the graph.

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 equation
A linear equation is a type of algebraic equation that represents a straight line when graphed on a coordinate plane. The standard form of a linear equation is \( y = mx + b \), where:
  • \( y \) is the dependent variable
  • \( x \) is the independent variable
  • \( m \) is the slope of the line
  • \( b \) is the y-intercept
The equation given in the exercise, \( y = x + 4 \), is a classic example of a linear equation.
slope-intercept form
The slope-intercept form of a linear equation is a powerful way to quickly understand the properties of the line represented by the equation. The form is \( y = mx + b \), where:
  • \( m \) represents the slope or the steepness of the line.
  • \( b \) represents the y-intercept, which is where the line crosses the y-axis.
The provided equation, \( y = x + 4 \), is already in this form with \( m = 1 \) and \( b = 4 \). This makes it easier to graph and understand how the line behaves.
y-intercept
The y-intercept of a line is the point where the line crosses the y-axis. In the slope-intercept form \( y = mx + b \), the y-intercept is given by \( b \). For our equation, \( y = x + 4 \), the y-intercept \( b \) is 4. This means the line will cross the y-axis at the point \( (0, 4) \). Finding the y-intercept is crucial because it provides a starting point for drawing the line on a graph.
slope
The slope of a line represents how steep the line is. The slope is often denoted as \( m \) and is calculated as the ratio of the rise (change in \( y \)) to the run (change in \( x \)). In the slope-intercept form \( y = mx + b \), \( m \) is the slope. For the equation \( y = x + 4 \), the slope \( m \) is 1. This means for every unit increase in \( x \), \( y \) also increases by 1 unit. Understanding the slope helps to determine the angle of the line and how it inclines.

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

Simplify. $$9^{3 / 2}$$

Simplify. $$16^{3 / 4}$$

Use the ZERO feature or the INTERSECT feature to approximate the zeros of each function to three decimal places. $$f(x)=|x+1|+|x-2|-3$$

Consider the function \(\int\) given by $$ f(x)=\left\\{\begin{array}{ll} -2 x+1, & \text { for } x<0 \\ 17, & \text { for } x=0 \\ x^{2}-3, & \text { for } 0

Use the ZERO feature or the INTERSECT feature to approximate the zeros of each function to three decimal places. $$f(x)=2 x^{3}-x^{2}-14 x-10$$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Discrete 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.