You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.)

Question

2012 value $950
Rate $350 increase per year

V(t)=??

Answer 1

you know that y=mt+b is the line which starts at b and grows by m for each successive value of t.

So, where does V start (when t=0), and how much does it grow when t increases by 1? That is, for each year?

Answer 2

V starts at 950?

Answer 3

Upon rereading the problem, I must revise my answer. You are given a point in 2012 (where t=2): (2,950)

and also the slope, or change each year. That is, m=350

So, using the point-slope form,

V(t) = 350(t-2)+950

Answer 4

So would that be my final answer or would I have to distribute?

Answer 5

depends how specific your teacher is.
To me, any correct form of the equation will do.
If you teacher specified the slope-intercept form, then yeah, expand it out.
But the point-slope form shows just how you got the equation, not just how well you can manipulate expressions.

Answer 6

Okay thank you. Here is another example with different numbers. Can you tell me if this is correct

You are given the dollar value of a product in 2012 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 0 represent 2010.)

250t+500

Is this the point slope form as well

Answer 7

2012 value is $550 and rate is $150 increase

Answer 8

150t+250*** my answer

Answer 9

looks good