Algebra 1
Algebra 1
1st Edition
ISBN: 9780078884801
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These…
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are…
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) ge…
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
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Chapter 3.1, Problem 37PPS
To determine

Determine the equation x2  =  10  +  2y3 is a linear equation or not. Write in Standard form.

Expert Solution & Answer
Check Mark

Answer to Problem 37PPS

Yes, this is a linear equation.

Standard form: 3x−4y−60=0

Explanation of Solution

Given:

The equation: x2  =  10  +  2y3

Concept Used:

A linear equation is any equation that can be written in the form. ax+b=0 . Where a and b are real numbers and x is a variable. This form is sometimes called the standard form of a linear equation.

No variable in a linear equation is raised to a power greater than 1. Linear equations are those equations that are of the first order.

Standard form of Linear Equation is Ax+By+C  =  0 , where A, B and C are any integer.

Calculation:

The equation: x2  =  10  +  2y3

Rewrite the equation in standard form.

Step 1: Multiply each term of the equation by the LCM 6 of the denominators 2 and 3.

  x2  =  10  +  2y36  ·  x2  =  6  ·  10  +  6  ·  2y33x  =  60  +4y  3x  −4y  −60  =  60  −60+4y−4y  [ Subtract  60&4y  from  both  sides ]3x−4y−60=0

The equation is now in standard form where A = 3, B = − 4 and C = − 60.

Yes, this is a linear equation.

Thus, yes, this is a linear equation. Standard form: 3x−4y−60=0

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Chapter 3.1, Problem 36PPS
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Chapter 3 Solutions

Algebra 1

Ch. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 58PPSCh. 3.1 - Prob. 60HPCh. 3.1 - Prob. 68STPCh. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2CYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYP
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Prob. 15HPCh. 3.6 - Prob. 16HPCh. 3.6 - Prob. 17HPCh. 3.6 - Prob. 18HPCh. 3.6 - Prob. 1ACYPCh. 3.6 - Prob. 1BCYPCh. 3.6 - Prob. 1CCYPCh. 3.6 - Prob. 2ACYPCh. 3.6 - Prob. 2BCYPCh. 3.6 - Prob. 19STPCh. 3.6 - Prob. 20STPCh. 3.6 - Prob. 21STPCh. 3.6 - Prob. 22STPCh. 3.6 - Prob. 23SRCh. 3.6 - Prob. 24SRCh. 3.6 - Prob. 25SRCh. 3.6 - Prob. 26SRCh. 3.6 - Prob. 27SRCh. 3.6 - Prob. 28SRCh. 3.6 - Prob. 29SRCh. 3.6 - Prob. 30SCh. 3.6 - Prob. 31SCh. 3.6 - Prob. 32SCh. 3.6 - Prob. 33SCh. 3.6 - Prob. 34SCh. 3.6 - Prob. 35SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 15QCCh. 3 - Prob. 16QCCh. 3 - Prob. 17QCCh. 3 - Prob. 18QCCh. 3 - Prob. 19QCCh. 3 - Prob. 20QCCh. 3 - Prob. 21QCCh. 3 - Prob. 22QCCh. 3 - Prob. 23QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - 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