Question

to increase her number of students, the instructor put a coupon in the local paper offering to waive the one - time fee for new students. what is the value of the coupon?

Explanation:

Step1: Find the linear equation of the cost

Assume the cost equation is \(y = mx + b\), where \(x\) is the number of lessons, \(y\) is the total cost.
Using two points \((1,50)\) and \((2,80)\):
The slope \(m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{80 - 50}{2 - 1}=30\).
Substitute \(m = 30\) and \((x = 1,y = 50)\) into \(y=mx + b\):
\(50=30\times1 + b\), so \(b = 20\).
The equation is \(y = 30x+20\).

Step2: Determine the coupon value

The \(y -\)intercept \(b = 20\) represents the one - time fee. If the coupon waives the one - time fee, the value of the coupon is \(\$20\).

Answer:

\(\$20\)