Linear Function
When two variables are related, their relationship can be expressed as a function. More specifically, if when one variable increase or decrease at a constant rate as the other variable increases or decreases, the two variables form a linear relationship that can be represented by a linear function on a coordinate plane.
Typical Form:
To graph a linear relationship on a coordinate plane, we will set the independent variable as 𝑥, and the dependent variable as 𝑦.
The typical form of such linear function is: 𝒚 = 𝒎𝒙 + 𝒃
Features:
A linear function would be shown as a straight line on the coordinate plane.
𝑏 represents the y-intercept (value of 𝑦 when 𝑥 = 0)
𝑚 represents the slope of the function
When 𝑚 has a greater absolute value, the line would be steeper.
But when 𝑚 has a smaller absolute value, the line would be flatter.
For instance, when 𝑚 = ∞, there will be a vertical line. While when 𝑚 = ∞, the line will instead be horizontal.
(The graph on the right is the linear function 𝑦 = 𝑥 + 1, 𝑤h𝑒𝑟𝑒 𝑚 = 1 𝑎𝑛𝑑 𝑏 = 1)
Parallel and Perpendicular Functions:
Example Question:
