The Equation Of A Straight Line
The Equation Of A Straight Line |
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MathsDirect |
The standard form for the equation of a straight line is
where m is the gradient and c 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). |
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If we apply the gradient formula |
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| This method can be generalized, so
that a line with gradient m, passing through the point (x1,y1),
has the equation
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Example
| Find the equation of the line L with
passing through the point (-1,2). |
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| 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.
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| Go to Case 2 | Return to Co-ordinate Geometry Tutorial Contents |
