/*! 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 39 Write the equation in slope-inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 39

Write the equation in slope-intercept form. Then graph the equation. $$ x+y=0 $$

Short Answer

Expert verified
The slope-intercept form of the given equation is \(y = -x\). The graph is a straight line passing through the origin (0,0) and sloping downwards from left to right.

Step by step solution

01

Convert to Slope-Intercept Form

To convert the equation to slope-intercept form, isolate \(y\). Subtract \(x\) from both sides of the equation. The result is \(y = -x\). Therefore, the slope-intercept form of the equation is \(y = -x\).
02

Identify the Slope and the y-intercept

The slope of the line \(m\) is the coefficient of \(x\) in the equation. In this case, \(m = -1\). The y-intercept \(b\) is the constant term in the equation. In this case, \(b = 0\). The y-intercept is the point where the line crosses the y-axis.
03

Graph the Equation

To graph the equation, first plot the y-intercept, which is at the point (0,0). Then, since the slope is -1, for every 1 unit increase in \(x\) (moving to the right on the x-axis), decrease \(y\) by 1 unit (moving down on the y-axis). Plot this point and draw a straight line that passes through both points.

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.

Graphing Equations
Graphing equations allows us to visualize mathematical relationships on a coordinate plane. When we graph linear equations, we look to plot points that represent solutions to the equation. These points usually form a straight line, hence the name "linear."
  • We begin by identifying key components, such as the slope and y-intercept, from the equation in slope-intercept form.
  • The initial point we plot is the y-intercept, where the line crosses the y-axis.
  • From this intercept, we utilize the slope to determine the position of another point on the graph.
  • Each increase in the x-coordinate by 1 unit results in a corresponding change in the y-coordinate determined by the slope.
Graphing is an important skill used in many fields, aiding in visual comprehension and analysis of data.
Linear Equations
Linear equations are algebraic expressions that represent straight-line relationships between variables. They are typically written in the form \(ax + by = c\). Solving these equations often involves finding pairs of values that satisfy the equation, which form points on a graph.
  • In two variables, linear equations describe lines in a plane.
  • When we manipulate linear equations into slope-intercept form, \(y = mx + b\), we simplify graphing by easily identifying slope \(m\) and y-intercept \(b\).
  • These equations can be solved algebraically by finding the value of one variable in terms of others, or graphically by representing them as lines and determining intersections.
Understanding linear equations is a fundamental aspect of algebra and is integral to studying higher mathematics, providing a basis for understanding more complex relationships.
Slope and Y-Intercept
The slope and y-intercept are crucial components in understanding and graphing linear equations.
  • The slope \(m\) indicates the steepness of a line and its direction of increasing or decreasing. It is calculated as "rise over run," or the change in \(y\) divided by the change in \(x\).
  • A positive slope means the line ascends from left to right, while a negative slope indicates it descends.
  • The y-intercept \(b\) is the point at which the line crosses the y-axis. It represents \(y\) when \(x\) is zero and acts as a starting point for graphing.
  • By knowing both the slope and y-intercept, one can accurately draw the graph of an equation by plotting the intercept and using the slope for direction.
These concepts are essential tools in analyzing linear relationships graphically and algebraically, providing insight into how variables relate to each other.

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

LOGICAL REASONING In Exercises \(56-59\), tell whether the statement is true or false. Justify your answer. The \(x\) -intercept of the graph of \(3 x+5 y=30\) is 10

Find the slope of the graph of the linear function \(f\). $$ f(-2)=-1, f(2)=6 $$

Find the \(x\) -intercept and the \(y\) -intercept of the graph of the equation. $$3 y=6 x+3$$

Is the given number a solution of the inequality? $$4 x-1>10 ; 3$$

find the quotient. $$ 54 \div 9 $$
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

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.