Chapter 4, Problem 3CR

To determine

Write a linear function.

Answer to Problem 3CR

The linear function is $f=x-5.$

Explanation of Solution

Given information:

Given values are

  $f(10)=5,f(2)=-3.$

So given points are (10,5) and (2,-3).

Calculation:

Formula :

In general slope intercept equation of a line or linear function is,

  $y=mx+b$ ….1

where $m$ is the slope of the line and $b$ is the y-intercept.

Finding $m$:

The slope of the lineor a linear function is the ration of the change of $y$ over the change in $x$ between any two points on the line.To find the slope between the points (10,5) and (2,-3)

  $\begin{array}{c}\text{slope=change}\text{in}y/\text{change}\text{in}x.\\ m=(y_{2-}{y}_1)/(x_2-x_1).\\ m=(-3-5)/(2-10).\\ m=-8/-8.\\ m=1.\end{array}$

Substituting $m=1$ in equation (1),

  $y=x+b.$ ….2

Finding $b$ :

Since given value is (10,5) so substituting 10 for $x$ and 5for $y$ in equation (2).

  $\begin{array}{l}5=10+b.\\ b=5-10.\\ b=-5.\end{array}$

Substituting the $b=-5$ in equation (2),

  $y=x-5.$ so,

The linear function with given values (10,5) and (2,-3) is $f=x-5.$