/*! 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 54 Find the intercepts. Then graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 54

Find the intercepts. Then graph by using the intercepts, if possible, and a third point as a check. $$ 5 x-4 y=20 $$

Short Answer

Expert verified
The x-intercept is (4, 0) and the y-intercept is (0, -5). A third point is (2, -2.5).

Step by step solution

01

Find the x-intercept

To find the x-intercept, set y = 0en the equation and solve for x: 5x - 4(0) = 20 This simplifies to 5x = 20 Divide both sides by 5: x = 4 So, the x-intercept is (4, 0).
02

Find the y-intercept

To find the y-intercept, set x = 0en the equation and solve for y: 5(0) - 4y = 20 This simplifies to -4y = 20 Divide both sides by -4: y = -5So, the y-intercept is (0, -5).
03

Find a third point as a check

Choose another value for x to find a third point. Let鈥檚 choose x = 2.Substitute x = 2 into the equation: 5(2) - 4y = 20This simplifies to 10 - 4y = 20Subtract 10 from both sides: -4y = 10Divide both sides by -4: y = -2.5So, the third point is (2, -2.5).
04

Graph the intercepts and the third point

Plot the points (4, 0), (0, -5), and (2, -2.5) on the coordinate plane. Draw a line through these points to graph the equation. Verify that all points lie on the same straight line.

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 an equation is the point where the graph crosses the x-axis. This means the y-coordinate is 0 at this point. To find the x-intercept of a linear equation like 5x - 4y = 20, we set y to 0 and solve for x.

Here's the process:
  • Substitute y = 0 into the equation: 5x - 4(0) = 20.
  • This simplifies to 5x = 20.
  • Divide both sides by 5 to solve for x: x = 4.
So, the x-intercept is (4, 0). This is the point where the line crosses the x-axis.
y-intercept
The y-intercept is the point where the graph crosses the y-axis. At this point, the x-coordinate is 0. To find the y-intercept of the equation 5x - 4y = 20, we set x to 0 and solve for y.

Here鈥檚 how to find it:
  • Substitute x = 0 into the equation: 5(0) - 4y = 20.
  • This simplifies to -4y = 20.
  • Divide both sides by -4 to solve for y: y = -5.
So, the y-intercept is (0, -5). This is the point where the line crosses the y-axis.
graphing linear equations
Graphing linear equations involves plotting points on the coordinate plane and drawing a straight line through them. For the equation 5x - 4y = 20, we have already found the intercepts:
  • x-intercept: (4, 0)
  • y-intercept: (0, -5)
To ensure accuracy, it鈥檚 helpful to find a third point. Let鈥檚 choose x = 2:

  • Substitute x = 2 into the equation: 5(2) - 4y = 20.
  • This simplifies to 10 - 4y = 20.
  • Solve for y: -4y = 10; y = -2.5.
So, the third point is (2, -2.5). Now, plot all three points (4, 0), (0, -5), and (2, -2.5) on the coordinate plane. Draw a line through these points.
solving linear equations
Solving linear equations involves finding the values of variables that make the equation true. In the context of finding intercepts, we鈥檙e looking for x and y values where the graph crosses the axes.

For x-intercept:
  • Set y = 0 and solve for x.
  • In our example, 5x = 20 means x = 4.
For y-intercept:
  • Set x = 0 and solve for y.
  • In our example, -4y = 20 means y = -5.
These solutions help us understand where the graph intersects the axes and aids in graphing the linear equation accurately.
coordinate plane
The coordinate plane is a two-dimensional surface where we can plot points, lines, and curves. It is divided into four quadrants by the x-axis and y-axis. Each point on the plane is represented by an ordered pair (x, y).

For example, the point (4, 0) means:
  • 4 units to the right of the origin on the x-axis.
  • 0 units up or down on the y-axis.
Another point (0, -5) means:
  • 0 units to the right or left on the x-axis.
  • 5 units down on the y-axis.
Understanding the coordinate plane is essential for graphing equations and visualizing mathematical relationships.

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

Indicate which of the following equations have \(\left(-\frac{1}{3}, \frac{1}{4}\right)\) as a solution. a) \(-\frac{3}{2} x-3 y=-\frac{1}{4}\) b) \(8 y-15 x=\frac{7}{2}\) c) \(0.16 y=-0.09 x+0.1\) d) \(2(-y+2)-\frac{1}{4}(3 x-1)=4\)

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ 3 x+5 y+15=0 $$

Solve graphically and then check by solving algebraically. $$ 3 x-2=5 x-9 $$

Let \(\left(x_{1}, y_{1}\right)\) and \(\left(x_{2}, y_{2}\right)\) be two distinct points on the graph of \(y=m x+b .\) Use the fact that both pairs are solutions of the equation to prove that \(m\) is the slope of the line given by \(y=m x+b\) (Hint: Use the slope formula.)

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ r^{2} x=p y+5 $$
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Geometry

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.