A long distance phone service charges $7 a month plus $0.10 per minute of call time.
a) Write an equation in the form c=mt+b to represent the total monthly charge,.C , in dollars, in terms of the time, t, in minutes.
b) Identify and explain what the slope and the C-intercept mean.
$7 is constant
$0.10 is the rate of charge -- that is, the slope
The C intercept is the charge for t=0 minutes
Is this correct if so thanks
a) To write the equation in the form c=mt+b, we can break down the given information.
The monthly charge consists of a fixed cost of $7 and an additional cost per minute of call time, which is $0.10 per minute.
Let's use the variable C to represent the total monthly charge in dollars and t to represent the time in minutes.
The fixed cost of $7 does not change regardless of the call time, so it will be the y-intercept or the b term in the equation.
The additional cost per minute is $0.10, and since this cost increases with the time, it will be multiplied by the time in minutes (t) and represented as mt.
Combining these terms, the equation representing the total monthly charge, C, would be:
C = 0.10t + 7
b) In the equation C = 0.10t + 7, the slope (m) represents the additional cost incurred per minute of call time. The slope, in this case, is 0.10. This means that for every additional minute of call time, the total monthly charge increases by $0.10. It shows the rate at which the cost increases.
The C-intercept or y-intercept (b) represents the fixed cost component of the total monthly charge. In this case, the C-intercept is 7, which means that even if there is zero call time, there will still be a fixed monthly charge of $7. This fixed cost covers the minimum monthly fee for the long-distance phone service.