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
