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

Answer:

$y = 50x + 50$

Step-by-step 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

$m = \frac{y_2 - y_1}{x_2- x_1}$

$m = \frac{600 - 350}{11- 6}$

$m = \frac{250}{5}$

$m = 50$

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:

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

$y - 350 = 50x - 300$

$y = 50x - 300 + 350$

$y = 50x + 50$