# Linear Functions

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A linear function is a function in which one variable is related to another variable in a linear way. This implies that the variables are written in the form of a linear equation where the highest exponent of the variable is equal to 1. Linear functions are very commonly used in math, and in a linear function the dependent variable and the independent variable are related in such a way that they have a constant rate of change (slope). Linear functions form straight lines when graphed on a coordinate plane.

Example 1: Write the linear function which has slope equal to 2 and satisfies the point (2, 1).

Given: rate of change = slope = m = 2
Point = (2, 1)

Point –slope form of a line==> (y – y1) = m(x – x1)

Therefore we get: (y – 1) = 1(x – 2)
This gives: y – 1 = x – 2
Simplifying the equation we get: y = x – 2 + 1 ==> y = x - 1

Hence we get the linear function as y = x – 1.

Example 2: Write the linear function which has slope equal to 3 and satisfies the point (3, -2).

Given: rate of change = slope = m = 3
Point = (3, -2)

Point –slope form of a line==> (y – y1) = m(x – x1)

Therefore we get: (y + 2) = 3(x – 3)
This gives: y + 2 = 3x – 9
Simplifying the equation we get: y = 3x – 9 - 2 ==> y = 3x - 11

Hence we get the linear function as y = 3x – 11.