Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Write A Linear Equation

1. A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. Write a linear equation for the salesperson’s
monthly wage W in terms of monthly sales S.

Solution:

Let W = salesperson's monthly wage

W = 5,000 + 0.07S

Correct?

2. A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced.
Its value at that time is expected to be $2000. Write a
linear equation giving the value V of the equipment
during the 10 years it will be in use.

I need help setting up the linear equation for question 2.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Write A Linear Equation

First is correct.

second: The drop in value is 24000 - 2000 over ten years, so divide that by 10 to get the rate of decrease, is the negative m value.  You have an intercept (24000) so the equation follows from that.

B

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Write A Linear Equation

First is correct.

second: The drop in value is 24000 - 2000 over ten years, so divide that by 10 to get the rate of decrease, is the negative m value.  You have an intercept (24000) so the equation follows from that.

B

Very good, Bob. Thank you.

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Write A Linear Equation

First is correct.

second: The drop in value is 24000 - 2000 over ten years, so divide that by 10 to get the rate of decrease, is the negative m value.  You have an intercept (24000) so the equation follows from that.

B

m = (24,000 - 2,000)/10

m = 2,200

I think the point we need is (year, sales).

I understand this to be (10, 24,000).

I now use the point-slope formula.

y - y_1 = m(x - x_1)

y - 24,000 = 2,200(x - 10)

Is this correct so far?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

Re: Write A Linear Equation

(10, 24000) is not a point.  You can use (0,24000) or (10, 2000)

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Write A Linear Equation

(10, 24000) is not a point.  You can use (0,24000) or (10, 2000)

Bob

Thanks for making the correction. Math is like a puzzle.