Introduction
- Given a set of coordinates such as:
x 0 50 100 y 5 35 65 - We can plot these on a graph:
- If all the points can be connected by a straight line then the relationship between x and y can be represented by the equation:
- Where:
- m = the gradient of the slope.
- b = the point that the line intercepts the y axis.
Calculating the equation for the straight line
- Calculating m:
- The value for m can be found by calculating the gradient of the line:
- Calculating b:
- If we know the value of y when x is 0, then b = y
- In the above example we are given the coordinate (0, 5)
- so b = 5
- If we do not know the value of y when x is 0, then:
- given a known coordinate, such as: (50, 35), and the gradient: 0.6
- then we plug these into our line equation:
- And solve to find that b = 5
- If we know the value of y when x is 0, then b = y
- Our equation for this straight line is therefore:
code (Python)
import math
def findEquation(p1, p2):
deltaY = p2[1] - p1[1]
deltaX = p2[0] - p1[0]
if deltaX == 0:
return math.inf, 0
else:
m = deltaY / deltaX
b = p1[1] - m * p1[0]
return m, b
m, b = findEquation([50, 35], [100, 65])
print(f'y = {m}x + {b}') # prints y = 0.6x + 5.0