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 an initial value and a rate of change? Use examples of your own to explain the process.

Answer 1

Answer: The process to create linear equation is given below.

Case 1: When 2 data points are given.

Let the two data ints be $(x_1,y_1)$ and $(x_2,y_2)$.

Then the linear equation is defined by the formula,

$y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$    ..... (1)

For example: Let the two points be (2,-1) and (-4,2). Then we get,

$y+1=\frac{2+1}{-4-2} (x-2)$

$y+1=\frac{3}{-6} (x-2)$

$2y+2=-x+2$

$2y=-x$

$y=\frac{-1}{2}x$

Case 2: When the initial value and rate of change is given.

Let the initial value be $(x_1,y_1)$ and slope is m. The rate of change is know as slope.

Then the linear equation is defined by the formula,

$y-y_1=m(x-x_1)$    ..... (2)

For example: Let the initial point be (4,5) and rate of change is 2. Then we get,

$y-5=2(x-4)$

$y-5=2x-8$

$y=2x-3$

Hence, the equation (1) and (2) are the formula to create a linear equation.