Coordinate geometry combines algebra and geometry. The discovery of coordinate geometry was a very important stage in the history of math. It brought a higher order to math. It also opened avenues for further math development. To learn more read the article Introduction to Coordinate Geometry.
The figure below is a graph of a straight line. Let us see how to find out the specific algebraic equation for this line.
First the gradient or slope of the line needs to be determined. Only two points on the line are needed for this.
Any two points on the line may be used for the purpose. I will use the two points that are marked on the line. (1.5,0) is the x-intercept and (0,–3) is the y-intercept.
Using the gradient formula for two points
m = (y2 – y1)/(x2 – x1)
m = (–3 – 0)/(0 – 1.5)
m = –3 / –1.5
m = 2
Gradient can also be known by observing the line. As the given line rises from left to right, its gradient is positive. The two marked points clearly show that there is a vertical rise of 3 for a horizontal run of 1.5. This is shown in blue dashes lines. Gradient is obtained by dividing rise by run.
m = rise/run
m = 3/1.5
m = 2
Gradient for a straight line is constant. It remains same and never changes. P(x,y) represents any point on the line. Using gradient formula again with points (1.5,0) and (x,y).
m = (y – 0)/(x – 1.5)
2 = y/(x – 1.5)
2(x – 1.5) = y
2x – 3 = y
2x – y = 3
2x – y = 3 is equation of the given straight line.
Use indepth geometric visualization to improve your math learning. Geometry is highly imaginative and coordinate geometry is where geometry meets algebra. It is a relationship that is both interesting and amusing. It is your gateway into the territory of higher math.
There are alternative ways of finding out the equation of a straight line. Read an excellent and colorful article on MathsIsFun to learn more