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?

Part 1) The rate of change is

Part 2) The equation of the line into slope intercept form is

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

step 2

Find the equation of the line into slope-intercept form

we know that

where

m is the slope

b is the y-intercept

we have that

point A(1, 75,000)

substitute

The equation of the line is

step 3

What will Tom's salary be in ten years?

For x=10 years

Substitute in the linear equation

answer: y - 3 = 4/11(x - 11)

step-by-step explanation:

the equation of a straight line can be represented in the point slope form as

y - y1 = m( x - x1)

where

m = slope = (change in the value of y in the vertical axis) / (change in the value of x in the horizontal axis)

the given slope of the line is 4/11 and the point through which the line passes is (11,3)

we would substitute m = 4/11, x1 = 11 and y1 = 3 into y - y1 = m( x - x1) to get the equation in the point slope form. it becomes

y - 3 = 4/11(x - 11)

for the slope intercept form, the equation is y = mx + c

where c is the intercept. to find c, we will substitute

m = 4/11, x = 11 and y = 3 into y = mx + c. it becomes

3 = 4/11 × 11 + c

3 = 4 + c

c = 3 - 4 = -1

the equation becomes

y = 4x/11 - 1