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, so we need 2x
• When x is 0, y is already 1. So +1 is also needed
• And so: y = 2x + 1

Here are some example values:

x	y = 2x + 1
-1	y = 2 × (-1) + 1 = -1
0	y = 2 × 0 + 1 = 1
1	y = 2 × 1 + 1 = 3
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 slope-intercept equation of a straight line:

Slope (or Gradient)	Y Intercept

Example: y = 2x + 1

• 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