Question

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

Answer 1

Given two (different) points, there is only one line passing through them. So, the linear equation modelling your dataset would be the line passing through the two data points.

In order to find the line, you can use the following equaiton: given two points $A = (A_x, A_y)\ ,B=(B_x,B_y)$, the line passing through them is given by

$\dfrac{y-A_y}{B_y-A_y} = \dfrac{x-A_x}{B_x-A_x}$

For example, given the points $A = (1,1)$ and $B = (5,7)$, you have

$\dfrac{y-1}{7-1} = \dfrac{x-1}{5-1} \iff \dfrac{y-1}{6} = \dfrac{x-1}{4} \iff 4(y-1) = 6(x-1)$

Now, if you want, you can rearrange this in the form

$4y-4 = 6x-6 \iff 4y = 6x-2 \iff y = \dfrac{3x}{2} - \dfrac{1}{2}$