let the linear function of the total calling time x (in minutes) be

f(x) = mx + b, where m is the slope, b is in y-intercept

we know that the slope m = -0.13 thus f(x) = -0.13x + b

there is 27.99 in credit remaining on the card after 23 minutes of calls that is for x = 23 min

f(23) = 27.99 we use this to find 'b'

-0.13*(23) + b = 27.99

b = 27.99 + 0.13*23

b = 30.98

now we know the that the function is

f(x) = - 0.13x + 30.98

how much credit will there be after 34 minutes of calls?

we find the answer by putting x = 34 in f(x)

f(34) = - 0.13*34 + 30.98

f(34) = 26.56

after 34 minutes of calls there will be 26.56 in credit remaining.