You can obtain the slope in many different ways.
Given 2 points on the line.
For example: A(1,2) B(4,6)
The slope = (y2 -y1) / (x2-x1)
= ( 6-2) / (4-1) = 4/3
==> The slope = 4/3.
Method (2): Given the equation of the line.
==> y= mx + a The slope is m.
2y - 3x + 4 = 0
==> 2y = 3x -4
==> y = (3/2)x - 4/2
==> y= (3/2)x - 2
The slope is (3/2).
This depends on what information you already have.
The easiest way to find this is if you are given the coordinates of two points on the line. Assuming they are in (x,y) form, you can use the slope formula:
slope = (y1 - y2)/(x1 - x2)
That gives you the vertical change (rise) over the horizontal change (run) and that is the defintion of slope.
There are 2 common methods to determine the slope of the line:
- putting the equation of the line in the slope intercept form: y = mx + n, where m represents the slope and n the y intercept;
- applying point-point method.
For instance, if we want to determine the slope of a line that is given by the equation y = 5x + 2, we'll apply the first method. The slope is the coefficient of x, so the slope is m = 5.
Also, if we want to find out the slope of the line that is passes through the points (2,3) and (5,8), we'll apply the 2nd method:
m = (8-3)/(5-2)
m = 5/3