Linear Equations

2014/9/16

Linear Equations

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Linear Equations
A linear equation is an equation for a straight line

These are all linear equations: y = 2x+1

5x = 6+3y

y/2 = 3 ­ x

Let us look more closely at one example:

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
Here are some example values:

http://www.mathsisfun.com/algebra/linear-equations.html

x

y = 2x + 1

­1

y = 2 × (­1) + 1 = ­1

0

y = 2 × 0 + 1 = 1

1

y = 2 × 1 + 1 = 3
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Linear Equations

2

y = 2 × 2 + 1 = 5

Check for yourself that those points are part of the line above!

Different Forms
There are many ways of writing linear equations, but they usually have constants (like "2" or
"c") and must have simple variables (like "x" or "y").

Examples: These are linear equations: y = 3x ­ 6 y ­ 2 = 3(x + 1) y + 2x ­ 2 = 0 5x = 6 y/2 = 3
But the variables (like "x" or "y") in Linear Equations do NOT have:
Exponents (like the 2 in x2)
Square roots, cube roots, etc

Examples: These are NOT linear equations: y2 ­ 2 = 0 3√x ­ y = 6 x3/2 = 16

Slope-Intercept Form
The most common form is the slope­intercept equation of a straight line :

http://www.mathsisfun.com/algebra/linear-equations.html

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Linear Equations

Slope (or Gradient)

Y Intercept

Example: y = 2x + 1
(Our example from the top, which is in Slope­Intercept form)
Slope: m = 2
Intercept: b = 1

Play With It !

You can see the effect of different values of m and b at Explore the Straight Line Graph

Point-Slope Form
Another common one is the Point­Slope Form of the equation of a straight line:

y ­ y1 = m(x ­ x1)

Example: y ­ 3 = ¼(x ­ 2) x1 = 2 http://www.mathsisfun.com/algebra/linear-equations.html 3/6

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Linear Equations

y1 = 3 m = ¼

General Form
And there is also the General Form of the