/*! 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 79 Sketch the graph of each linear ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 79

Sketch the graph of each linear equation. Be sure to find and show the \(x\) - and \(y\) -intercepts. $$ x+y=80 $$

Short Answer

Expert verified
(80,0) and (0,80); Graph the line through these points.

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y = 0 in the equation and solve for x:\[ x + 0 = 80 \]\[ x = 80 \]So, the x-intercept is at (80, 0).
02

Find the y-intercept

To find the y-intercept, set x = 0 in the equation and solve for y:\[ 0 + y = 80 \]\[ y = 80 \]So, the y-intercept is at (0, 80).
03

Plot the intercepts

Plot the points (80, 0) and (0, 80) on the coordinate plane.
04

Draw the line

Draw a straight line through the points (80, 0) and (0, 80) to sketch the graph of the equation \( x + y = 80 \).

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 of a linear equation is where the line crosses the x-axis. At this point, the y-coordinate is zero.
To find the x-intercept:
  • Set y to 0 in the equation.
  • Solve for x.
For example, in the equation
\[ x + y = 80 \]
set y = 0:
\[ x + 0 = 80 \]
which simplifies to
\[ x = 80 \]
So, the x-intercept is at (80, 0). This means the line crosses the x-axis at the point (80, 0).
y-intercept
The y-intercept of a linear equation is where the line crosses the y-axis. Here, the x-coordinate is zero.
To find the y-intercept:
  • Set x to 0 in the equation.
  • Solve for y.
For the equation
\[ x + y = 80 \]
set x = 0:
\[ 0 + y = 80 \]
which simplifies to
\[ y = 80 \]
So, the y-intercept is at (0, 80). This means the line intersects the y-axis at (0, 80).
coordinate plane
The coordinate plane is a two-dimensional surface where each point is defined by a pair of numerical coordinates. These are usually labeled as (x, y).
The coordinate plane has two axes:
  • The x-axis (horizontal)
  • The y-axis (vertical)
The point where they intersect is called the origin, labeled (0, 0). When graphing a line, you use this plane to plot points, such as the x-intercept and y-intercept.
For example, to graph the line from the equation
\[ x + y = 80 \]
You'd plot the x-intercept (80, 0) and the y-intercept (0, 80) on this plane.
linear equation
A linear equation is an equation that makes a straight line when it is graphed on the coordinate plane. Its general form is:
\[ Ax + By = C \]
where A, B, and C are constants.
In the given equation
\[ x + y = 80 \]
A is 1, B is 1, and C is 80. This equation represents a straight line.
To graph a linear equation:
  • Find the x-intercept by setting y = 0 and solving for x.
  • Find the y-intercept by setting x = 0 and solving for y.
  • Plot the intercepts on the coordinate plane.
  • Draw a line through these points.
This creates a visual representation of the linear equation.

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

What equation expresses the area of a square as a function of its side?

Solve each problem. Perpendicular Tangents A circle of radius 5 intersects a circle of radius 12 so that the tangent lines at the points of intersection are perpendicular. What is the distance between the centers of the circles?

Growth Rate One measurement of the quality of a mutual fund is its average annual growth rate over the last 10 years. The function \(r=\left(\frac{P}{10,000}\right)^{1 / 10}-1\) expresses the average annual growth rate \(r\) as a function of the present value \(P\) of a investment of \(\$ 10,000\) made 10 years ago. An investment of \(\$ 10,000\) in Fidelity's Contrafund in 2008 was worth \(\$ 23,580\) in 2018 (Fidelity Investments, www.fidelity.com). What was the annual growth rate for that period? Write \(P\) as a function of \(r\)

Find the domain and range for the function \(f(x)=-\sqrt{x-2}+3\)

Find the equation of a circle with center (0,1) and radius \(3 .\)
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.