Question

When given 2 data points, how would you use this information to create a linear equation, how would you create a linear equation if you were given and initial value and a rate of change? Use examples of your own to explain the process.

Answer 1

First question: When given 2 data points, how would you use this information to create a linear equation?

This calls for the point-slope form:
(y-b) = m(x-a) 
We are given a point (a,b) and (x,y). We can plug in these points to solve for m, the slope. 
For example:
Points given: (1,1) and (2,3)
We can say that (1,1) is (a,b) and (2,3) is (x,y)
(y-b) = m(x-a)
(3-1)= m(2-1)
2 = m 
Therefore: 
(y-1) = 2(x-1)

2nd Question: 
how would you create a linear equation if you were given and initial value and a rate of change
Since we have the slope and a coordinate, we can use slope-intercept form to solve for b: 
Let's say rate of change (slope, or m) is 2, and our given point is (3,5)
Slope-intercept form: 
y= mx + b            Plug in m, x and y
5 = 2(3) + b 
5 = 6 + b      
-1 = b
plugging in b and m: 
y = 2x - 1