Let y be the total cost for x minutes of phone calls.
The slope-intercept form of a linear relation between x and y is:
Where m is the slope of the line and represents the rate of change of y with respect to x, and b is the y-intercept of the line and represents the initial value.
The first plan has a rate of change of $0.12 for each minute, and an initial value (which is the fee when 0 minutes of calls are used) of $11. Then, the equation that describes this plan is:
The second plan has an initial value of $15 and a rate of change of $0.08. The equation for this one, is:
If x is such that both plans have the same cost, then:
Therefore, the two plans have the same cost when the number of minutes of calls is equal to 100.