Question

bonnie is part of the cinema movie club. in october she saw 5 movies and spent a total of $30.00. in november she saw 10 movies and spent a total of $50.00. (hint: try making ordered pairs or putting the information in a table and working from there) equation: __________ cost of watching 17 movies: __________

Explanation:

Step1: Assume linear - cost model

Let the cost $y$ be a linear function of the number of movies $x$, $y = mx + b$. We have two points $(x_1,y_1)=(5,30)$ and $(x_2,y_2)=(10,50)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 5,y_1 = 30,x_2 = 10,y_2 = 50$ into it: $m=\frac{50 - 30}{10 - 5}=\frac{20}{5}=4$.

Step3: Calculate the y - intercept $b$

Substitute $m = 4$ and the point $(5,30)$ into $y=mx + b$. We get $30=4\times5 + b$. Then $30 = 20 + b$, and $b=30 - 20=10$.

Step4: Write the equation

The linear equation is $y = 4x+10$.

Step5: Calculate the cost for 17 movies

Substitute $x = 17$ into $y = 4x + 10$. Then $y=4\times17+10=68 + 10=78$.

Answer:

Equation: $y = 4x + 10$
Cost of watching 17 movies: $\$78$