This common feature that distinguishes the points on a particular line is given by the relationship between x and y.
Each point on the x-y axis has two unique numbers (called coordinates). So, point A (a,b) or pt. B (aCos z, aSin z). The points on a line all have a certain relationship. Since there are infinite number of points on the line and we can’t show all of them, we take a general coordinate and call it (x,y) and then show the relationship between them which will then hold for all the points on that line. Let us see the simplest example: y = x which is the equation of a straight line. In the diagram two points are shown: (a,a) & (b,b). Since the equation is y=x so the two coordinates will be equal. In fact any number like (1,1) or 2,2 or 7.1,7.1 will all fall on this line.
We end up with an isosceles right angled triangle and
So, the angle the line y = x makes with the x axis is 45 degrees.
Basic Equation of the Straight Line
And that gives us the general equation of the Straight line
y = m x
m is also called the slope of the line
Imagine the line shows you a mountain slope and now it will be clear why the word slope is used. And mathematically it is precisely measured by tan z,