/*! 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 156 Find the intercepts for each equ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 156

Find the intercepts for each equation. \(x-y=1\)

Short Answer

Expert verified
The intercepts are (1, 0) and (0, -1).

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. Start with the original equation:\[ x - y = 1 \]When y is 0:\[ x - 0 = 1 \]\[ x = 1 \]Therefore, the x-intercept is (1, 0).
02

- Find the y-intercept

To find the y-intercept, set x to 0 in the equation and solve for y. Start with the original equation:\[ x - y = 1 \]When x is 0:\[ 0 - y = 1 \]\[ -y = 1 \]Multiply both sides by -1 to solve for y:\[ y = -1 \]Therefore, the y-intercept is (0, -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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

x-intercept
To find the x-intercept of a linear equation, you need to set the value of y to zero. This will show where the line crosses the x-axis.
Start with your given equation and substitute y with 0:
For example, with the equation \(x - y = 1\), set \(y = 0\):
\(x - 0 = 1\)
Then, simplify and solve for x:
\(x = 1\)
Thus, your x-intercept is (1, 0). This is the point where the graph touches the x-axis at x=1 while y remains 0.
This concept is very useful in graphing because it helps in drawing the first point of the line on the coordinate plane.
y-intercept
To find the y-intercept of a linear equation, set the value of x to zero. This will show where the line crosses the y-axis.
Take the original equation and substitute x with 0:
For example, with the equation \(x - y = 1\), set \(x = 0\):
\(0 - y = 1\)
Then, simplify and solve for y:
\(-y = 1\)
Multiply both sides by -1 to isolate y:
\(y = -1\)
Thus, your y-intercept is (0, -1). This is the point where the graph touches the y-axis at y=-1 while x remains 0.
Finding the y-intercept helps identify where the line begins on the vertical axis.
solving linear equations
Solving linear equations is a fundamental skill in math. Linear equations form straight lines when graphed.
To solve them, you can use various methods such as:
  • Substitution: Replacing variables with values to simplify the equation
  • Elimination: Combining equations to cancel out a variable
  • Graphing: Plotting the equation on a graph to find intercepts
Consider the equation: \(x - y = 1\)
When we set y to 0 to find the x-intercept, we solved the simplified equation \(x = 1\).
When we set x to 0 to find the y-intercept, we simplified to \(-y = 1\) and then \(y = -1\).
These methods help you understand how each variable affects the equation and find precise points on the graph where the line crosses axes.
Understanding how to solve linear equations is key to mastering algebra and many real-world applications.

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 \(y+7=0,\) point(1,-1)

Find an equation of a line perpendicular to the given line and contains the given point. Write the equation in slope-intercept form. line \(y=-x+5,\) point(3,3)

Find the equation of each line. Write the equation in slope-intercept form. Perpendicular to the line \(y\) -axis, point (-6,2)

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

Determine whether each ordered pair is a solution to the inequality \(y
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Probability and 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.