Equation of a straight line

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
• 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