We assume a linear relationship between the cost, y, and the time, x, in the form: y=ax+b, where a is the charge rate in $ per minute and b is a standing fixed charge.
So we have two equations: 19.41=52a+b and 45.65=380a+b. Subtract the first eqn from the second: 328a=26.24, so a=26.24/328=$0.08 or 8 cents per minute (answer for part A).
We can find b by substituting a=0.08 in the first equation: 19.41=0.08*52+b, so b=19.41-4.16=$15.25.
Susan's plan (answer to part B) is based on y=0.08x+15.25. Check that the second eqn fits: 45.65=0.08*380+15.25.