Question

Fill in the missing numbers to complete the linear equation that gives the rule for this table.

y =____x + ____

Answer 1

The missing numbers: y = –23x + 22

Solution:

Let us find the linear equation to the given data.

To find y in terms of x.

First calculate the common difference for y.

–47 – (–24) = –23

–70 – (–47) = –23

–93 – (–70) = –23

So, the common difference = –23

$a_1=-24-(-23)=-1$

General expression for a linear equation using arithmetic sequence.

$y(x)=a_1+(x-1)d$

$y(x)=-1+(x-1)-23$

       $=-1-23x+23$

       $=-23x+22$

$y(x)=-23x+22$

Hence the missing numbers: y = –23x + 22.