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:

[tex]y = 50x + 50[/tex]

Step-by-step explanation:

Given

x = years since 1992.

y = value of pin

This means that

[tex]x = 1[/tex] ----- in 1992

[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex] ---- in 1997

[tex]x_2 = 11;[/tex] [tex]y_2 = 600[/tex] ---- in 2002

Required

Determine the line equation in slope intercept form

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

[tex]m = \frac{y_2 - y_1}{x_2- x_1}[/tex]

[tex]m = \frac{600 - 350}{11- 6}[/tex]

[tex]m = \frac{250}{5}[/tex]

[tex]m = 50[/tex]

The equation is then calculated using:

[tex]y - y_1 = m(x - x_1)[/tex]

Recall that

[tex]x_1 = 6[/tex]; [tex]y_1 = 350[/tex]

[tex]m = 50[/tex]

So, we have:

[tex]y - 350 = 50(x - 6)[/tex]

[tex]y - 350 = 50x - 300[/tex]

[tex]y = 50x - 300 + 350[/tex]

[tex]y = 50x + 50[/tex]

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