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=(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=(2+1)/(-4-2) (x-2)`

`y+1=(3)/(-6) (x-2)`

`2y+2=-x+2`

`2y=-x`

`y=(-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.