What is a Linear equation?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A linear equation is an equation that consists of terms that are either constants or products of a variable raised to to the power 1 and a constant.

There is a one-to-one relation between each of the variables in a linear equation. For example, y = 2x + 3 is a linear equation. Each of the variables in the equation is raised to the power one. The graph of this equation is a straight line as for each value of x or y there is only one corresponding value of y or x.

On the other hand in the equation y = 3x^2 is not a linear equation as the variable x is raised to power 2. For each value of y, there are two corresponding values of x; this leads to a graph that is a parabola.

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ssarfraz | Student, Professional | (Level 2) Honors

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A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable. Linear equations can have one or more variables.

Basically, It is a equation for making a straight line.

Examples of a linear equation are as follows:-

y = 3x - 6

y - 2 = 3(x+1)

Example: y = 2x+1 is a linear equation:

The graph of y = 2x+1 is a straight line

  • When x increases, y increases twice as fast, hence 2x
  • When x is 0, y is already 1. Hence +1 is also needed
  • So: y = 2x + 1
                           
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malkaam | Student, Undergraduate | (Level 1) Valedictorian

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A linear equation is a significant part of algebra, whereby each term is either a constant or the product of a constant and is the power of a single variable.

It is merely an equation that helps to form a straight line, and includes slope and intercepts. 

In order to get a complete detail of how such equations are used to from a line, the link is given below:

Sources:
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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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A linear equation is a problem that is written in the y= mx + b form. 

The m and the b can change but the x stays the same.

Ex:

5x + 10 is a linear equation.

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jess1999 | Student, Grade 9 | (Level 1) Valedictorian

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A linear equation is a function that forms a line. A linear equation also needs to fit the equation y = mx + b

y = the point for y

m = slope

x = the point for x

b = y intercept

In a linear equation, there needs to be a slope that is constant throughout. For example if the slope is two, then it needs to continue to be 2 throughout the graph.

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sid-sarfraz | Student, Graduate | (Level 2) Salutatorian

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Linear Equation

Basically a linear equation is an equation that forms a straight line. It is an equation that can contain as many variables as possible but only on one condition that is exponential power must be 1.

Linear Equation is a mathematical expression that has an equal sign and linear expressions.

Where as, variables are basically are shown by alphabets and whose value is unknown.

For example;

8x + 6y = 0

OR

ax + by + c= 0

Or

2x +3y +5z = 0

Characteristics of Linear equations

  • It has one or two variables.
  • No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction.
  • When you find pairs of values that make the linear equation true and plot those pairs on a coordinate grid, all of the points for any one equation lie on the same line. Linear equations graph as straight lines.

In a linear equation in x and y, x is called x is the independent variable and y depends on it. We call y the dependent variable.

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kanikajain6 | (Level 1) eNoter

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when we equate two algebric expressions using the sign of equality it forms an equation.linear equations are first degree equations and may contain one or more variables.

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glendamaem | Student | (Level 1) Honors

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A linear equation is a an equation that is composed by numbers, variables or terms; it does not matter how long this equation is as long as the highest exponential power of the elements is one. The graph of this type of equation is a straight line and it is represented by the equation y=mx+b; wherein m is the slope and b is the y-intercept.

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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A linear equation is the equation of a straight line. A line can be represented by the equation y = mx + b. M represents the slope while b represents the y-intercept (where the line crosses the y-axis).

An example of a linear equation is y = 3x + 7. 3 would be the slope of the line and positive 7 is where the line crosses the y-axis.

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