Question

use the table for exercises 13 and 14. a movie streaming service charges a set fee for membership each month, plus an additional fee for the number of movies streamed each month. this table shows the total charge for different numbers of movies. 13. movies write the slope - intercept form of the equation that models the linear relationship in the table. (lesson 4 - 1) 14. movies interpret the meaning of the slope and y - intercept in the context of the situation. (lesson 4 - 1)

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(2,14)\) and \((x_2,y_2)=(4,17)\).
\(m=\frac{17 - 14}{4 - 2}=\frac{3}{2}=1.5\)

Step2: Find the y - intercept

Use the slope - intercept form \(y = mx + b\). Substitute \(m = 1.5\), \(x = 2\), and \(y = 14\) into the equation.
\(14=1.5\times2 + b\)
\(14 = 3 + b\)
\(b=14 - 3=11\)

Step3: Write the equation

The slope - intercept form is \(y=mx + b\). Substitute \(m = 1.5\) and \(b = 11\).
\(y = 1.5x+11\)

Answer:

\(y = 1.5x + 11\)