Question

The price of a share of stock in XYZ Corporation was $ 74 two weeks ago. Seven weeks ago, the price was $59 a share. Write a linear equation to find the price "p" of a share of XYZ Corporation stock "w" from now.

Answer 1

`p=3w+80`

Explanation:

`p\rightarrow` represent price of a share.

`w\rightarrow` represent weeks.

The linear equation in slope intercept form can be represented as:

`p=mw+b`

where
`m` is slope of line or rate of change of price of share and
`b` is the y-intercept or initial value of share price.

We can construct two points using the data given.

Price was $ 74 two weeks ago.
`(-2,74)`

Price was $ 59 seven weeks ago.
`(-7,59)`

Using the points we can find slope
`m` of line.

`m=(p_2-p_1)/(w_2-w_1)`

`m=(59-74)/(-7-(-2))`

`m=(-15)/(-5)`

`m=3`

Using point slope form of linear equation to write the equation using a given point.
`y-y_1=m(x-x_1)`

Using point
`(-2,74)`.

`p-74=3(w-(-2))`

⇒
`p-74=3(w+2)`

⇒
`p-74=3w+6`

Adding 74 to both sides:

⇒
`p-74+74=3w+6+74`

⇒
`p=3w+80`

The linear equation to find the price "p" of a share of XYZ Corporation stock "w" weeks from now is:

`p=3w+80`