The equation of a straight line can be given in two main forms:
| y = mx + c | called the gradient/intercept form | e.g. y = 2x + 3 |
| ax + by + c = 0 | called the general form |
e.g. 3x + 4y + 6 = 0 |
The equation of a straight line can be worked out in several ways depending on the information given about the line.
Equation of line given the gradient and the y-intercept
If the gradient of a line is given and the y-intercept is known, then this information can be substituted into the formula
|
y = mx + c where m is the gradient c is the y-intercept. |
The equation can then be simplified into one of the two forms above.
See example
Equation of line given the gradient and a point it passes through
If the gradient of a line is given and the coordinates of a point the line passes through are known this information can be substituted into the formula:
|
y − y1= m(x − x1) where m is the gradient (x1, y1) is a point on the line. |
See example
Equation of line given two points it passes through
If two different points that the line passes through are known this information can be substituted into the formula:
|
(x1, y1) is one point on the line and (x2, y2) is another. |
See example
An alternative way, rather than use the complicated formula above is to work out the gradient of the line joining the two points and then use the formula y − y1= m(x − x1)
The last two formulas are often given to students in tests and examinations.
