The cost for 7 dance lessons is $82. the cost for 11 lessons is $122. write a linear equation to find the total cost c for l dance lessons.

First, find the slope of the line representing the total cost.

The slope of the line thru (7, $82) and (11, $122) is

$122-$82

m = = $40/4 per hour, or $10 per hour.

11-7

Now write the linear equation. I'm choosing to use the slope-intercept form:

y = mx+ b. Here, we have m = $10 per hour and the point (7, $82)

Then $82 = ($10 per hour)(7 hrs) + b. Then b = $82-$70, or $12.

Thus, the desired line is

y = ($10.hr)x + $12.

Looks like there is an up-front fee of $12 along with the hourly fee of $10.