Answer:
$20
Step-by-step explanation:
Let
x ----> the number of lessons
y ----> the total cost
Find the slope of the linear equation
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the graph
(1,50) and (2,80)
substitute
[tex]m=\frac{80-50}{2-1}[/tex]
[tex]m=\$30\ per\ lesson[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept or initial value
we have
[tex]m=30[/tex]
[tex]point\ (1,50)[/tex]
substitute
[tex]50=30(1)+b\\b=20[/tex]
the linear equation is
[tex]y=30x+20[/tex]
The term [tex]b=\$20[/tex]
represent the y-intercept or one-time fee for new students
therefore
The value of the coupon is $20
