Question

Tom just received a new job offer. He is told that his starting salary will be $75,000 per year. He is told his salary will probably be $81,000 in four years. We'll use this information to try to anticipate his future earnings in any given year.Assume that Y= Tom's salary amount in dollars and x= the number of years worked. Step 1.Use the data given to find the rate of change, or the salary increase per year.( hint: compute the slope.) We are now going to use a line to model Tom's salsry growth. Step 2. Use the data given and the slope value from Step 1 to write the slope-intercept form of the line. Step 3. Based on your equation from Step 2, What will Tom's salary be in ten years?

Answer 1

The increment in salary is $1500 each year. The slope intercept form is
`y=1500x+75000` and the salary in 10 years will be $90000.

Explanation:

Consider the provided information.

The starting is $75,000 per year.

Let x is the number of years worked and y is Tom's salary amount in dollars.

When he has 0 yr of experience, his salary is $75000 per year.

it can be written as (0,75000).

His salary will probably be $81,000 in four years.

It can be written as (4,81000).

STEP 1:

Find the rate of change by using the formula slope=
`m=(rise)/(run)`.

Determine the rise by subtracting 75000 from 81000.

Rise = 81000 - 75000 = 6000

Now determine the run by subtracting 0 from 4.

Run = 4 - 0 = 4

Substitute the respective values in the above formula.

`slope=m=(6000)/(4)\\slope=m=1500`

Therefore, the rate of change, or the salary increase per year is $1500.

STEP 2:

Write the slope intercept form by using the formula:

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

Substitute m = 1500 and
`(x_1,y_1)=(0,75000)` on the above formula.

`(y-75000)=1500(x-0)\\y-75000=1500x\\y=1500x+75000`

Thus, the slope intercept form is
`y=1500x+75000`.

STEP 3:

The salary in 10 years. can be calculated as:

Substitute the value of x = 10 in
`y=1500x+75000`.

`y=1500(10)+75000\\y=15000+75000\\y=90000`

Hence, the salary in 10 years will be $90000.

Answer 2

Part 1) The rate of change is
`2,000\ \$/year`

Part 2) The equation of the line into slope intercept form is
`y=2,000x+73,000`

Part 3) Tom's salary would be
`\$93,000` in ten years

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`

step 2

Find the equation of the line into slope-intercept form

we know that

`y=mx+b`

where

m is the slope

b is the y-intercept

we have that

`m=2,000\ \$/year`

point A(1, 75,000)

substitute

`75,000=(2,000)(1)+b`

`b=75,000-2,000=73,000`

The equation of the line is

`y=2,000x+73,000`

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`