Liberty the job offer is: $40,000 per year with raises of $4,500 annually. Fidelity Investment, the job offer is: $50,000 per year with raises of $3,500 annually.a)      State the linear...

Liberty the job offer is: $40,000 per year with raises of $4,500 annually. Fidelity Investment, the job offer is: $50,000 per year with raises of $3,500 annually.

a)      State the linear equations to describe the two job offers.

b)      State the slope and the Y-intercept for each equation stated in part a

c)       What does the slope represent in each one of your equation?

d)      What does the y-intercept represent in each one of your equation?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

At Liberty the job offer is an initial pay of $40000 followed by a raise of $4500 per year. The function that gives the salary in year x in this case is y = 40000 + 4500*x

On the other hand Fidelity Investment offers an initial pay of $50000 which is increased by $3500 every year. The function for salary in year x after joining is y = 50000 + 3500*x

The slope of the equation obtained for Liberty is 4500 and that for Fidelity is 3500.

The slope represents the annual increase in salary.

The y-intercept in each of the equations represents the initial salary.

najm1947's profile pic

najm1947 | Elementary School Teacher | (Level 1) Valedictorian

Posted on

If salary is 'y' and period lapsed in years is taken as 'x' (whole numbers only) then initial salary will be the y-intercept 'c' whereas increament will be the slope 'm' of the straight line equation y=mx+c

a) In case of, the linear equatios are:

Liberty,  y=4500x+40000

Fidelity Investment,  3500x+50000

b) The slope and Intercepts are as under respectively

Liberty: slope = 4500, intercept= 40000

Fidelity Investment: slope = 3500, intercept = 50000

c) The slope represents Annual Raise in salary

d) y-intercept represents the initial salary

e) The table for initial 15 years is given below. For first year x=0 and the values are given as x, year and salary (y) for Liberty and Fidelity Investment

 x .. Year .. Liberty Salary (y) .. Fidelity Investment Salary (y)
 0 .... 1 ..... 40,000 ................ 50,000
 1 .... 2 ..... 44,500 ................ 53,500
 2 .... 3 ..... 49,000 ................ 57,000
 3 .... 4 ..... 53,500 ................ 60,500
 4 .... 5 ..... 58,000 ................ 64,000
 5 .... 6 ..... 62,500 ................ 67,500
 6 .... 7 ..... 67,000 ................ 71,000
 7 .... 8 ..... 71,500 ................ 74,500
 8 .... 9 ..... 76,000 ................ 78,000
 9 ... 10 .... 80,500 ................ 81,500
10 .. 11 .... 85,000 ................ 85,000
11 .. 12 .... 89,500 ................ 88,500
12 .. 13 .... 94,000 ................ 92,000
13 .. 14 .... 98,500 ................ 95,500
14 .. 15 .. 103,000 ................ 99,000

 

 

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