/*! 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 27 Find the intercepts and graph th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 27

Find the intercepts and graph them. $$ 2 x-52 y=10 $$

Short Answer

Expert verified
X-intercept: (5, 0); Y-intercept: (0, -5/26). Plot these on the graph to find the line.

Step by step solution

01

Find the x-intercept

To find the x-intercept, set the value of \( y = 0 \) in the equation and solve for \( x \). The equation becomes \( 2x - 52(0) = 10 \), which simplifies to \( 2x = 10 \). Divide both sides by 2 to find \( x \): \[ x = \frac{10}{2} = 5 \]So, the x-intercept is \( (5, 0) \).
02

Find the y-intercept

To find the y-intercept, set the value of \( x = 0 \) in the equation and solve for \( y \). The equation becomes \( 2(0) - 52y = 10 \), which simplifies to \( -52y = 10 \). Divide both sides by -52 to find \( y \): \[ y = \frac{10}{-52} = -\frac{5}{26} \]So, the y-intercept is \( (0, -\frac{5}{26}) \).
03

Plot the intercepts on the graph

On a coordinate plane, plot the points for the intercepts found in the previous steps. The x-intercept \( (5, 0) \) is located on the x-axis at 5, and the y-intercept \( (0, -\frac{5}{26}) \) is slightly below the x-axis on the y-axis. These points can be used to draw the line representing the equation.

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 where a line crosses the x-axis of a graph. At this point, the value of \( y \) is always zero because it's located exactly on the x-axis. To find the x-intercept of an equation, we set \( y = 0 \) and solve for \( x \). In our equation, \( 2x - 52y = 10 \), substituting \( y = 0 \) yields \( 2x = 10 \). Solving for \( x \) gives us \( x = 5 \), meaning the x-intercept is \( (5, 0) \).
Understanding the x-intercept allows us to take an initial step in graphing linear equations. It's like finding one endpoint of a ruler when you know how long the ruler is.
y-intercept
The y-intercept occurs where a line crosses the y-axis. Here, the value of \( x \) is zero because we've moved vertically to intersect with the y-axis. To find this intercept, we set \( x = 0 \) in the equation and solve for \( y \). Using the equation \( 2x - 52y = 10 \), replacing \( x \) with 0 results in \( -52y = 10 \). Solving for \( y \), we find \( y = -\frac{5}{26} \), giving us the y-intercept \( (0, -\frac{5}{26}) \).
The y-intercept provides another point to plot, giving us the second anchor needed to draw a straight line for a linear equation on a graph.
graphing linear equations
Graphing linear equations involves plotting points and drawing a straight line through them on a coordinate plane. The intercepts are crucial in this process because they give us two definite points to outline a line. From our previous steps, our x-intercept is \( (5, 0) \) and our y-intercept is \( (0, -\frac{5}{26}) \).
To draw the line:
  • Plot the x-intercept \( (5, 0) \) on the x-axis.
  • Plot the y-intercept \( (0, -\frac{5}{26}) \) on the y-axis.
  • Connect these two points with a ruler to form a straight line.
This line represents all the solutions to the equation \( 2x - 52y = 10 \). Linear equations like these form a straight line because for every point \( (x, y) \) on this line, the equation holds true. By plotting intercepts and connecting them, you visually express the relationship between \( x \) and \( y \).

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

Graph using the slope and \(y\) -intercept. $$ y=0 $$

Is the ordered pair a solution to the given inequality? $$ -3 x+y>2 ;(0,2) $$

Graph the solution set. $$ y \geq-2 x+1 $$

Graph using the slope and \(y\) -intercept. $$ 2 x+32 y=3 $$

Graph the linear function and state the domain and range. $$ g(x)=6 x+2 $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation

Applied Mathematics

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.