Answer:
Part 1) The rate of change is
Part 2) The equation of the line into slope intercept form is ![y=2,000x+73,000](https://tex.z-dn.net/?f=y%3D2%2C000x%2B73%2C000)
Part 3) Tom's salary would be
in ten years
Step-by-step explanation:
Let
x ------> the number of years worked
y -----> Tom's salary amount in dollars
we have the points
A(1, 75,000) and B(4,81,000)
step 1
Find the rate of change (slope)
The slope is equal to
![m=(81,000-75,000)/(4-1)=2,000\ \$/year](https://tex.z-dn.net/?f=m%3D%2881%2C000-75%2C000%29%2F%284-1%29%3D2%2C000%5C%20%5C%24%2Fyear)
step 2
Find the equation of the line into slope-intercept form
we know that
![y=mx+b](https://tex.z-dn.net/?f=y%3Dmx%2Bb)
where
m is the slope
b is the y-intercept
we have that
![m=2,000\ \$/year](https://tex.z-dn.net/?f=m%3D2%2C000%5C%20%5C%24%2Fyear)
point A(1, 75,000)
substitute
![75,000=(2,000)(1)+b](https://tex.z-dn.net/?f=75%2C000%3D%282%2C000%29%281%29%2Bb)
![b=75,000-2,000=73,000](https://tex.z-dn.net/?f=b%3D75%2C000-2%2C000%3D73%2C000)
The equation of the line is
![y=2,000x+73,000](https://tex.z-dn.net/?f=y%3D2%2C000x%2B73%2C000)
step 3
What will Tom's salary be in ten years?
For x=10 years
Substitute in the linear equation
![y=2,000(10)+73,000=\$93,000](https://tex.z-dn.net/?f=y%3D2%2C000%2810%29%2B73%2C000%3D%5C%2493%2C000)