/*! 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 36 Find the \(x\) - and \(y\) -inte... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 36

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ 5 x+2 y=10 $$

Short Answer

Expert verified
x-intercept: (2, 0), y-intercept: (0, 5)

Step by step solution

01

Find the x-intercept

The x-intercept is found by setting y = 0 and solving for x. Start with the equation 5x + 2y = 10. Substitute y with 0 to get 5x + 2(0) = 10, which simplifies to 5x = 10. Solving for x gives x = 2. Therefore, the x-intercept is at (2, 0).
02

Find the y-intercept

The y-intercept is found by setting x = 0 and solving for y. Start with the equation 5x + 2y = 10. Substitute x with 0 to get 5(0) + 2y = 10, which simplifies to 2y = 10. Solving for y gives y = 5. Therefore, the y-intercept is at (0, 5).
03

Plotting the intercepts on the graph

On the Cartesian plane, plot the points for the x-intercept (2, 0) and the y-intercept (0, 5).
04

Draw the line

Draw a straight line through the points (2, 0) and (0, 5). This line represents the graph of the equation 5x + 2y = 10.

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 the point where the graph crosses the x-axis. To find it, set y = 0 in the equation and solve for x. For our example, we start with the equation: 5x + 2y = 10. Substituting y = 0, we have: 5x + 2(0) = 10, which simplifies to 5x = 10. Solving for x gives: x = 2. Therefore, the x-intercept is the point (2, 0). Remember, the x-intercept always has a y-value of 0 because it lies on the x-axis.
y-intercept
The y-intercept of a linear equation is the point where the graph crosses the y-axis. To determine it, set x = 0 in the equation and solve for y. Using the same equation: 5x + 2y = 10. Substituting x = 0, we get: 5(0) + 2y = 10, which simplifies to 2y = 10. Solving for y yields: y = 5. Thus, the y-intercept is the point (0, 5). It's crucial to understand that the y-intercept will always have an x-value of 0, because it is located on the y-axis.
Cartesian plane
A Cartesian plane is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). The point where these axes intersect is called the origin, with coordinates (0, 0). When graphing equations, points are plotted based on their coordinates (x, y):
  • The x-coordinate shows the position along the horizontal axis.
  • The y-coordinate shows the position along the vertical axis.
For the given equation 5x + 2y = 10, we plot the x-intercept (2, 0) and the y-intercept (0, 5). On a Cartesian plane, every point corresponds to a unique coordinate pair.
solving linear equations
Solving linear equations involves finding the values of the variable(s) that satisfy the equation. Here are the general steps:
  • Identify the given equation. For instance, 5x + 2y = 10.
  • To find the intercepts, set one variable to zero and solve for the other.
  • Use elementary algebraic operations (addition, subtraction, multiplication, and division).
After determining the intercepts: x = 2 (when y = 0) and y = 5 (when x = 0), you can plot these points on the Cartesian plane. Finally, draw a straight line through the plotted points. This line visualizes the solution set of the 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

Three points that lie on the same straight line are said to be collinear. Consider the points \(A(3,1), B(6,2),\) and \(C(9,3) .\) Find the slope of segment \(A B\)

For each function, find \((a) f(2)\) and \((b) f(-1) .\) See Examples 4 and \(5 .\) $$ f=\\{(-1,-5),(0,5),(2,-5)\\} $$

Find the \(x\) - and \(y\) -intercepts. Then graph each equation. $$ 4 y=3 x $$

Solve each equation for \(y\). $$ 3 x+4 y=12 $$

Suppose a factory can have no more than 200 workers on a shift, but must have at least 100 and must mamufacture at least 3000 units at minimum cost. The managers need to know how many workers should be on a shift in onder to produce the required units at minimal cost. Linear programming is a method for finding the optimal (best possible) solution that meets all the conditions for such problems. Let \(x\) represent the number of workers and y represent the mumber of units manufactured. Work Exercises \(47-52\) in order. Write three inequalities expressing the conditions given in the problem.
See all solutions

Recommended explanations on Math Textbooks

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Applied Mathematics

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.