/*! 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 19 Determine the intercepts and gra... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 19

Determine the intercepts and graph each linear equation. $$x-y=2$$

Short Answer

Expert verified
x-intercept: (2, 0), y-intercept: (0, -2)

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y to 0 and solve for x. Start with the equation: \[ x - y = 2 \] Since y is 0, substitute it into the equation: \[ x - 0 = 2 \] Therefore, \[ x = 2 \] So, the x-intercept is (2, 0).
02

Find the y-intercept

To find the y-intercept, set x to 0 and solve for y. Start with the equation: \[ x - y = 2 \] Since x is 0, substitute it into the equation: \[ 0 - y = 2 \] Therefore, \[ -y = 2 \] which simplifies to \[ y = -2 \] So, the y-intercept is (0, -2).
03

Graph the equation

Plot the x-intercept (2, 0) and the y-intercept (0, -2) on a graph. Draw a straight line through these points to represent the equation. The graph of the equation \[ x - y = 2 \] will be a straight line passing through the points (2, 0) and (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.

Understanding the x-intercept
The x-intercept of a linear equation is the point where the line crosses the x-axis. This means the y-value at this point is zero. To find the x-intercept, we set y to 0 in the equation and solve for x. Let's look at our example equation: \( x - y = 2 \) When y is set to 0, we get: \( x - 0 = 2 \) This simplifies to: \( x = 2 \) Therefore, the x-intercept is at the point (2, 0). This means the graph will touch the x-axis at 2, and you can plot this point on your graph.
Understanding the y-intercept
The y-intercept of a linear equation is the point where the line crosses the y-axis. This means the x-value at this point is zero. To find the y-intercept, we set x to 0 in the equation and solve for y. Using our example equation: \( x - y = 2 \) When x is set to 0, we get: \( 0 - y = 2 \) Which simplifies to: \( -y = 2 \) Dividing both sides by -1, we find: \( y = -2 \) So, the y-intercept is at the point (0, -2). This means the graph will touch the y-axis at -2, and you should plot this point on your graph.
Graphing linear equations
Graphing a linear equation involves plotting points and connecting them with a straight line. For an equation like \( x - y = 2 \), start by finding both intercepts. Plot the x-intercept (2, 0) and the y-intercept (0, -2) on the graph. Once these points are on the graph, simply draw a straight line through them. This line represents the equation.

Here's a quick checklist:
  • Find the intercepts.
  • Plot the intercepts on the graph.
  • Draw a straight line through these points.


This method works for any linear equation and helps visualize the relationship between x and y.
Solving linear equations
Solving linear equations means finding the values of x and y that satisfy the equation. There are various methods, including:
  • Substitution Method: Replace one variable in terms of another and solve.
  • Elimination Method: Add or subtract equations to eliminate one variable.
  • Graphical Method: Plot the equations and find the intersection point.


For our equation \( x - y = 2 \), we simplified it by setting y to 0 for the x-intercept and x to 0 for the y-intercept. Each solution step reduces the equation's complexity, making it easier to understand and graph.

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

In Exercises \(33-38\), determine whether the lines with the given equations are parallel, perpendicular, or neither. \(2 x+1=0\) \(-3 y-4=0\)

In Exercises \(1-6,\) find the slope of the line passing through the given pair of points. \((-5,2)\) and \((-1,-6)\)

Find the distance between the points given. $$(3,2) \text { and }(-2,-10)$$

In Exercises \(1-6,\) find the slope of the line passing through the given pair of points. \((7,-1)\) and \((3,3)\)

In Exercises \(1-6,\) find the slope of the line passing through the given pair of points. \((4,2)\) and \((4,-2)\)
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation

Calculus

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.