Blog Post #4

Hello, my name is Professor Amy Martinez and today I am going to attempt to teach you about linear growth. The first step in this process is to decide what the definition of linear growth it. Linear growth means that it grows by the same amount in each time step. This means that the growth is constant and when you have an equation involved it means that for each input that you enter into the equation there is exactly one output.
Now that we have an idea what linear growth is we can decide why it is important to understand in real life. Linear growth is very helpful to understand because it allows you to track progress on certain things and make predictions about how things will look in the future. For example, you could use linear growth in a business to track how much of a product you have been selling and how much money you are making. You could also use it to measure data of how much a person or something else has grown over a period of time and predict where it/they will be at in the future. You can also graph linear functions to have a physical view of what the growth of something looks like.
Linear growth is represented with a standard equation known as y=mx+b . The parent function for this equation looks like this:

These are what the symbols in the equation represent... 

m=slope or rate of change

b= starting value or "y-intercept" value

y= output value

x=input value

In order to find the slope, you can use data such as "x" and "y" inputs and calculate it. This equation for rate of change is represented by (y2-y1)/(x2-x1). This is a simple equation to find the rate of change, which in a graph is also represented by (rise/run). 

To find "b" or the y-intercept, you just have to find the point where the line on a graph passes over the y-axis, or where the x-value is zero. 

Linear equations can also be represented by the point-slope formula. This equation is y-y1=m(x-x1) In a situation where you are presented with this equation instead it is necessary to solve for "y" so that it is by itself and then you can use the slope to plug in a set of values to solve for "b". 

Now lets do a problem together! Use the table below to write a linear equation and graph the function. 

x	y
1	4
2	11
3	18
4	25

Step 1: Find the slope: (11-4) / (2-1) = 7 

Slope = 7

Step 2: Find "b": y=7x+b

... Plug in a coordinate and solve for "b" 

 4=7(1)+b 

-7  -7

b=-3

So... the equation is y=7x-3 

Step 3: Graph equation