Equation of Straight Line
Equation of Straight Lines (Recap)
You should know the following:
the equation of a horizontal line is in the form ;
the equation of a vertical line is in the form ;
In a sloped line , the equation is in the form , where is the gradient and is the y-intercept.
- we can find its gradient given the coordinates of two points on the line.
- the gradient formula is
- we can find the y-intercept of the by substituting and the new-found value of into the equation .
General Equation of a Sloped Line
Consider a general point lying on the same line in the above applet.
Since gradience of AP = gradient of AB, then,.
Multiplying both sides, by , we then have
Since , then the above becomes
In other words, the general equation of a sloped line passing through a point is