The Equation Of A Straight Line

MathsDirect

The standard form for the equation of a straight line is

where m is the gradient and the is the value of y where the line crosses the y-axis,( the y-intercept.) You should be familiar with this formula, from as long ago as Year 8!

At A-level, you need to be able to find the equation of a line in 2 situations

You are given the gradient and one point on the line,( not the intercept.)
You are given two points on the line.

Case 1

Suppose that you are told that a straight line has a gradient of 2 and passes through the point (1,3)		We want to find the equation that connects x and y at any point on the line, so we can pick a general point (x,y)
If we apply the gradient formula

This method can be generalized, so that a line with gradient m, passing through the point (x₁,y₁), has the equation

Example

Find the equation of the line L with passing through the point (-1,2)
Put the values into the formula remove the brackets on the bottom Cross multiply. Re-arrange to make y positive Tidy up, making y the subject.

Go to Case 2

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