Question

1. the cost for 7 dance lessons is $82. the cost for 11 lessons is $122. write a linear equation, slope - intercept form, to find the total cost c for l lessons.

c = 10l+12

1. use the equation in #11 to find the cost of 4 lessons.

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $x$ be the number of lessons $L$ and $y$ be the cost $C$. We have the points $(7,82)$ and $(11,122)$. So $m=\frac{122 - 82}{11 - 7}=\frac{40}{4}=10$.

Step2: Find the y - intercept

Using the slope - intercept form $y=mx + b$ (or $C = mL+b$), and substituting one of the points, say $(7,82)$ and $m = 10$ into it. We get $82=10\times7 + b$. Then $82=70 + b$, and $b=82 - 70=12$. So the linear equation is $C = 10L+12$.

Step3: Find the cost of 4 lessons

Substitute $L = 4$ into the equation $C = 10L+12$. Then $C=10\times4+12=40 + 12=52$.

Answer:

1. $C = 10L+12$
2. $52$