Gradient Formulas

a. Gradient formula from the points passed

The straight line through the points A(x₁, y₁) and B(x₂, y₂) has a gradient:

Example:
Please determine the gradient from a straight line through points A(2, 4) and B(3, 8)!

Answer:
x₁ = 2
y₁ = 4
x₂ = 3
y₂ = 8

So the gradient from a straight line through points A(2, 4) and B(3, 8) is 4

b. Gradient Formulas from a Straight Line Equation

There are 4 formulas to determine the gradient of the straight-line equation are:

The equation of a straight line: ax + by = c, then the gradient is m = -a/b.
The equation of a straight line: y = ax + b. then the gradient is m = a.
Lines parallel to the x-axis have the equation y = c, then the gradient m = 0.
The line parallel to the y-axis has the equation x = c, then it has no gradient.

Example:
Find the gradient of 2x + y = 5 !

Answer:
a = 2
b = 1

m = -a/b
m = -2/1
m = -2

So the gradient of the equation 2x + y = 5 is -2.

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