Question

restaurants in 2012, a popular pizza franchise had 2483 restaurants. in 2017, there were 2606 franchised restaurants. write an equation in point - slope form that represents the number of restaurants y that are franchised x years after 2010.

Explanation:

Step1: Determine the points

First, we need to find the values of \( x \) (years after 2010) and \( y \) (number of restaurants) for the given years.

For 2012: \( x = 2012 - 2010 = 2 \), \( y = 2483 \)

For 2017: \( x = 2017 - 2010 = 7 \), \( y = 2606 \)

So we have two points: \( (2, 2483) \) and \( (7, 2606) \)

Step2: Calculate the slope (\( m \))

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \)

Substituting the values: \( m=\frac{2606 - 2483}{7 - 2}=\frac{123}{5} = 24.6 \)

Step3: Use point - slope form

The point - slope form of a linear equation is \( y - y_1=m(x - x_1) \)

We can use the point \( (2, 2483) \) and \( m = 24.6 \)

Substituting into the formula: \( y - 2483=24.6(x - 2) \)

(We could also use the point \( (7, 2606) \), the equation would be \( y - 2606 = 24.6(x - 7) \))

Answer:

\( y - 2483 = 24.6(x - 2) \) (or \( y - 2606 = 24.6(x - 7) \))