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.
