Question 933700

 

a linear function:
{{{y=mx+b}}}

A). Write a linear function to describe this situation.

A lecturer with {{{9}}} years of experience is paid ${{{41350}}}. 

{{{x=9}}} and {{{y=41350}}}

{{{41350=m*9+b}}} ....eq.1

A lecturer with 15 years experience of teaching experience is paid ${{{46687}}}.

{{{x=15}}} and {{{y=46687}}}

{{{46687=m*15+b}}} ....eq.2

solve this system to find {{{m}}} and {{{b}}}

{{{41350=9m+b}}} ....eq.1
{{{46687=15m+b}}} ....eq.2
_________________.....subtract eq.1 from eq.2

{{{46687-41350=15m+b-(9m+b)}}}

{{{5337=15m+cross(b)-9m-cross(b)}}}

{{{5337=6m}}}

{{{5337/6=m}}}

{{{m=889.5}}}

go to eq.1 substitute m and solve for {{{b}}}

{{{41350=9*889.5+b}}} ....eq.1

{{{41350=8005.5+b}}}

{{{41350-8005.5=b}}}

{{{b=33344.5}}}

your equation is:

{{{y=889.5x+33344.5}}}


B). Use the function to determine the salary of a lecturer with {{{10}}} years of experience.

{{{x=10}}}
{{{y=889.5*10+33344.5}}}
{{{y=8895+33344.5}}}
{{{y=42239.5}}}

C). Estimate how many years of teaching experience a lecturer must have to earn a salary of ${{{44908}}}. 

{{{44908=889.5x+33344.5}}}

{{{44908-33344.5=889.5x}}}

{{{11563.5=889.5x}}}

{{{11563.5/889.5=x}}}

{{{13=x}}} years of teaching experience a lecturer must have to earn a salary of ${{{44908}}}