Question

Write a linear function f with f(-3)=1 and f(13)=5

Answer 1

`y = (1)/(4)x +(7)/(4)`

Explanation:

Given

`f(-3) = 1`

`f(13) = 5`

Required

Determine the linear function

A function is of the form:

`y = f(x)`

Writing the given parameters in (x,y) format, we have:

`f(-3) = 1` implies (-3,1)

`f(13) = 5` implies (13,5)

So, the x and y values are:

(-3,1) and (13,5)

i.e.

`(x_1,y_1) = (-3,1)`

`(x_2,y_2) = (13,5)`

First, we need to determine the slope using:

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

`m = (5 - 1)/(13 - -(3))`

`m = (4)/(13 +3)`

`m = (4)/(16)`

`m = (1)/(4)`

The equation is calculated as thus:

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

Where

`(x_1,y_1) = (-3,1)`

`m = (1)/(4)`

`y - 1 = (1)/(4)(x - (-3))`

`y - 1 = (1)/(4)(x +3)`

`y = (1)/(4)(x +3) + 1`

`y = (1)/(4)x +(3)/(4) + 1`

`y = (1)/(4)x +(3+4)/(4)`

`y = (1)/(4)x +(7)/(4)`