Finding the Formula for Linear Functions- Marisa Ewing

Lesson Plan- Finding the Formula for Linear Functions
Professor Ewing

In today's class, we will be learning to find the formula from linear functions.

First we will define what a linear function is.

A linear function is a function that looks like a straight line. It will intersect with the y intercept only once (b) and it has a constant rate of change, known as the slope (m). 

A linear function is defined by the formula

y = mx + b

y = output
m = slope
b = y intercept

These are all linear functions:

Finding the formula for a linear function requires a bit of information to start with; either two points that the line travels through, or one point the line travels through and the slope (m).

Let's do an example:

A linear function f(x) travels through the points (1,2) and (5,3). Find the formula of this function.

Step one to solving a problem like this is finding the slope (m). To do this, we must use the formula

Change in y

Change in x

Which also looks like:

y₂ – y₁

x₂ – x₁

So in this scenario, we would plug the two points into this forumula and solve to get the slope

3-2

5-1

When solved, we find that the slope is 1/2.

So now, our formula looks like this

y = (1/2)x + b

To find b, we plug one of the given points into this equation and solve for b

2 = (1/2)(1) +b

2 = (1/2) + b

3/2 = b

b is equal to 3/2, so our final formula is

y = (1/2)x + (3/2)