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Equation of a Straight Line

The equation of a straight line is usually written this way:

y = mx + b

(or "y = mx + c" in the UK see below)


Slope (or Gradient)	Y Intercept

y = how far up

x = how far along

m = Slope or Gradient (how steep the line is)

b = the Y Intercept (where the line crosses the Y axis)

Example 1

b = 1 (where the line crosses the Y-Axis)

Therefore y = 2x + 1

-1

–3

b = 0

This gives us y = –3x + 0
We do not need the zero!

Therefore y = –3x

What is the equation for a vertical line?
The slope is undefined ... and where does it cross the Y-Axis?

In fact, this is a special case, and you use a different equation, not "y=...", but instead you use "x=...", like this:

x = 1.5

You can see the effect of different values of m (the slope) and b (the y intercept) at Explore the Straight Line Graph

What we have been looking at is called the "slope-intercept" form.

The equation of a straight line can be written in other ways. Another popular form is:

y - y₁ = m(x - x₁)

Different Countries teach different "notation" (as sent to me by kind readers):

In the US and Canada the notation is:	y = mx + b
In the UK, Australia, Bahamas, Brunei, India, Indonesia, Ireland, Jamaica, Malaysia, Malta, Nepal, Pakistan, and South Africa:	y = mx + c
In Brazil, Denmark, Holland and Viet Nam:	y = ax + b
In China, Finland and Ukraine:	y = kx + b
In Greece:	ψ = αχ + β
In Italy:	y = mx + q
In Japan:	y = mx + d
In Latvia:	y = jx + t
In Romania:	y = gA + C
In Sweden:	y = kx + m

In your country:	let us know!

... but it all means the same thing, just different letters.