Question

If f(x) is a linear function, f(−2)=4, and f(1)=−1, find an equation for f(x)

Answer 1

`y = -(5)/(3)x+(2)/(3)`

Explanation:

Given

`f(-2) = 4`

`f(1) = -1`

Required

The equation of the function

The given parameters means that:

`(x_1,y_1) = (-2,4)`

`(x_2,y_2) = (1,-1)`

Calculate the slope (m)

`m = (y_2 -y_1)/(x_2 -x_1)`

`m = (-1-4)/(1--2)`

`m = (-5)/(3)`

The equation is then calculated using:

`y = m(x - x_1) + y_1`

This gives:

`y =(-5)/(3)(x--2)+4`

`y =(-5)/(3)(x+2)+4`

Open bracket

`y = -(5)/(3)x-(10)/(3)+4`

Take LCM

`y = -(5)/(3)x+(-10+12)/(3)`

`y = -(5)/(3)x+(2)/(3)`