let x1=7 lessons, y1 =$82, x2 = 11 lessons, y2 = $122, and x = 13 lessons
Also let y be total dollars to learn 13 lessons.
Now using 2 point form of line equation we get:
y- y1 = (y2-y1)/(x2-x1) * (x-x1)
y - 82 = (122-82)/(11-7) * (13-7)
y - 82 =60
y= 60+82
y = 142 dollars
So Lydia will have to pay $142 for 13 lessons.