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Linear Equation - A Graphical Explanation
The material below is designed for seniors in high school or below:
We often make real-life decisons when not given enough information. Given the information we have, we try to predict what the behavior or output will be based on the input data we do have. In other words, we try to formulate an equation for both the data we have and for data we have not collected.
This concept of fitting an equation with our observations or data is called modeling.
One of the simplest model is the linear graph which consists of a straight line.
When you hear equations, functions and graphs, they are based on descriptions on what we observe. Equations are based on mathematical relationships while graphs are pictorial illustrations of the mathematical relations. Functions are basically the output in terms of the input.
The notation is given as y=f(x) where y is our output and x is the input and f stands for function of the input x. For a linear relationship, it is described as y=bx plus c, where b is the slope and c is the y-intercept when x=0.
The video below described this relationship. All these are straight lines.
To describe horizontal lines, the equation is given as y=c. It is a constant. What device produces a constant. A battery is an example. The horizontal axis is time and the vertical axis is the battery voltage. For a short period of time, the battery appears to be constant.
To describe vertical lines, the equation is given as x=a (These lines are not functions since for each value of x there are multiple or infinite values of y).
We often make real-life decisons when not given enough information. Given the information we have, we try to predict what the behavior or output will be based on the input data we do have. In other words, we try to formulate an equation for both the data we have and for data we have not collected.
This concept of fitting an equation with our observations or data is called modeling.
One of the simplest model is the linear graph which consists of a straight line.
When you hear equations, functions and graphs, they are based on descriptions on what we observe. Equations are based on mathematical relationships while graphs are pictorial illustrations of the mathematical relations. Functions are basically the output in terms of the input.
The notation is given as y=f(x) where y is our output and x is the input and f stands for function of the input x. For a linear relationship, it is described as y=bx plus c, where b is the slope and c is the y-intercept when x=0.
The video below described this relationship. All these are straight lines.
To describe horizontal lines, the equation is given as y=c. It is a constant. What device produces a constant. A battery is an example. The horizontal axis is time and the vertical axis is the battery voltage. For a short period of time, the battery appears to be constant.
To describe vertical lines, the equation is given as x=a (These lines are not functions since for each value of x there are multiple or infinite values of y).
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