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.

Explanation:

Step1: Find the slope

The two points are $(7, 82)$ and $(11, 122)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here $x_1 = 7,y_1 = 82,x_2=11,y_2 = 122$. So $m=\frac{122 - 82}{11 - 7}=\frac{40}{4}=10$.

Step2: Find the y - intercept

Use the point - slope form $y - y_1=m(x - x_1)$ and then convert to slope - intercept form $y=mx + b$. Let's use the point $(7,82)$. Substitute $m = 10,x = 7,y = 82$ into $y=mx + b$. We get $82=10\times7 + b$. Solving for $b$: $82=70 + b$, so $b=82 - 70=12$.

Step3: Write the linear equation

The total cost $C$ for $L$ lessons in slope - intercept form is $C = 10L+12$.

Answer:

$C = 10L + 12$