/*! 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 153 Find the intercepts for each equ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 153

Find the intercepts for each equation. \(x+y=-2\)

Short Answer

Expert verified
The x-intercept is (-2, 0) and the y-intercept is (0, -2).

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y to 0 in the equation and solve for x. Starting with the equation: \[x + y = -2\]Set y to 0: \[x + 0 = -2\]Therefore, \[x = -2\]The x-intercept is \[(-2, 0)\]
02

Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Starting with the equation: \[x + y = -2\]Set x to 0: \[0 + y = -2\]Therefore, \[y = -2\]The y-intercept is \[(0, -2)\]

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.

x-intercept
The x-intercept is the point where the graph of an equation crosses the x-axis. At this point, the value of y is always 0.
To find the x-intercept of the equation, set y to 0 and solve for x. In our example equation, \( x + y = -2 \), we set y to 0: \[ x + 0 = -2 \]
Thus, \[ x = -2 \]
So, the x-intercept is at \( (-2, 0) \).
Finding the x-intercept helps understand how the graph behaves and provides a specific point through which the line passes.
y-intercept
The y-intercept is the point where the graph of an equation crosses the y-axis. At this point, the value of x is always 0.
To find the y-intercept of the equation, set x to 0 and solve for y. Using the same example equation, \( x + y = -2 \), we set x to 0: \[ 0 + y = -2 \]
This simplifies to: \[ y = -2 \]
So, the y-intercept is at \((0, -2)\).
Knowing the y-intercept is essential because it provides one of the points needed to plot the linear equation on a graph correctly.
linear equations
Linear equations are equations of the first degree, meaning they involve only the first power of the variable. The standard form of a linear equation is \( Ax + By = C \), where A, B, and C are constants.
In our example, \ x + y = -2 \, A is 1, B is 1, and C is -2.
Linear equations form straight lines when graphed.
Key characteristics of linear equations include:
  • They have constant rates of change.
  • They can be easily represented using slope-intercept form \( y = mx + b \).
  • The graphs show a straight line across the coordinate plane.
This knowledge of linear equations, x-intercepts, and y-intercepts empowers you to solve and graph any linear equation effectively!

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 an equation of a line parallel to the given line and contains the given point. Write the equation in slope-intercept form. line \(2 x-y=6,\) point (3,0)

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form. line \(y=\frac{3}{4} x-2,\) point(-3,4)

Find the equation of each line. Write the equation in slope-intercept form. Containing the points (2,7) and (3,8)

Graph the linear inequality \(y>4 x\)

Lester thinks that the solution of any inequality with \(\mathrm{a}>\) sign is the region above the line and the solution of any inequality with \(\mathrm{a}<\) sign is the region below the line. Is Lester correct? Explain why or why not.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Pure Maths

Read Explanation

Decision 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.