Linear Equation

A Linear Equation is a mathematical expression.  It is an algebraic equation where one variable depends on other. It is generally appears in below form:

y = 6x + 2 

The above equation is in the form of y = mx + b, where m and b are constant.

It is an equation that forms a straight line on a graph. In this particular equation, the constant m determines the slope or gradient of that line, and the constant term b determines the point at which the line crosses the y-axis, that is also known as the y-intercept. So, in the equation y = 6x + 2, slope m is 6 and y-intercept b is 2.

Linear equation is simple in manner and  each term in linear equation will not have 

• Exponents (or powers). For example, x²
• Multiplication or division of  each other. For example: "x" times "y" or xy; "x" divided by "y" or x/y
• A root sign or square root sign (sqrt). For example: √x or the "square root x"; sqrt (x) 

The following equations are  all linear equations:

i) y = 2x+1             ii)  9x = 6+3y               iii) y/4 = 9 - x

Linear equation will be in other form also. For example

i) y = 4                ii) 8x + 4 = 0                iii) y - 3 = ¼(x - 2)

The third example is in point-slope form [ y-y1 = m(x-x1) ]

 

Linear equation graph

(Photo courtesy: hotmath.com)

Solving a linear equation:

i)           4x + 8 = 20
             4x = 12
             x = 12/4
             x = 3

ii)        ( (x-2)/3 ) + 1 =  2x/7
           (x + 1)/3  =  2x/7
           7 (x + 1)  =  6x
           7x +7  =  6x
           7x - 6x  =  - 7
            x  =  - 7