Question

In 1992, Disney created a one-of-a-kind special pin. Each year, the pin’s value appreciates by a constant amount. In 1997, the pin was valued at $350. In 2002, it was valued at $600. Let x be the number of years since 1992 and y be the value of the pin in dollars. Write a linear equation in slope-intercept form that models this situation.

Answer 1

`y = 50x + 50`

Explanation:

Given

x = years since 1992.

y = value of pin

This means that

`x = 1` ----- in 1992

`x_1 = 6`;
`y_1 = 350` ---- in 1997

`x_2 = 11;`
`y_2 = 600` ---- in 2002

Required

Determine the line equation in slope intercept form

First, we need to determine the slope (m) of the line

`m = (y_2 - y_1)/(x_2- x_1)`

`m = (600 - 350)/(11- 6)`

`m = (250)/(5)`

`m = 50`

The equation is then calculated using:

`y - y_1 = m(x - x_1)`

Recall that

`x_1 = 6`;
`y_1 = 350`

`m = 50`

So, we have:

`y - 350 = 50(x - 6)`

`y - 350 = 50x - 300`

`y = 50x - 300 + 350`

`y = 50x + 50`