linear function help

Question

The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 36 minutes of calls is $19.96 , and the remaining credit after 49 minutes of calls is $18.14 . What is the remaining credit after 57 minutes of calls?

Answer 1

Great question!!

Let the horizontal axis (x) represent the number of minutes used and the vertical axis (y) represent the $ on the card. This would mean (36 , 19.96) and (49 , 18.14) are 2 points on the line. What's the equation of the line? What is y when x = 57?

Need more help? Let me know.

Answer 2

James,

you have to do two things:

(a) discover the linear formula

(b) use the formula to find out the answer

(a) any linear formula is y = mx + b, let’s discover m and b

we know

19.96 = m*36 + b

18.14 = m*49 + b

subtract them

1.82 = m*(-13)

solve for m

1.82 / -13 = m = -1.4

discover b by substituting for m

19.96 = (-1.4)36 + b

solve for b, then

(b) write the formula with the last bit of data:

Fill in the numbers for m and b,

y = m*57 + b

and solve for y.