Let's start by defining the variables:
Let x be the total calling time made with the card (in minutes).
Let y be the remaining credit on the card (in dollars).
We can use the given information to create two equations in slope-intercept form:
Equation 1: y = mx + b (for the data point (25, 26.25))
Equation 2: y = mx + b (for the data point (51, 22.35))
To solve for the equation of the line, we need to find the slope (m) and y-intercept (b) of each equation. We can use the two data points to create a system of two equations:
Equation 1: 26.25 = 25m + b
Equation 2: 22.35 = 51m + b
We can solve this system using elimination or substitution. Here's how to solve using substitution:
Solve Equation 1 for b:
b = 26.25 - 25m
Substitute this expression for b into Equation 2:
22.35 = 51m + (26.25 - 25m)
Simplify and solve for m:
22.35 = 26m + 26.25
-3.9 = 26m
m = -0.15
Now that we know the slope of the line is -0.15, we can substitute this value into either equation to solve for b. Let's use Equation 1:
26.25 = 25(-0.15) + b
b = 29.5
Therefore, the equation for the line is:
y = -0.15x + 29.5
To find the remaining credit after 65 minutes of calls, we can plug in x = 65 into the equation and solve for y:
y = -0.15(65) + 29.5
y = 20.75
Therefore, the remaining credit after 65 minutes of calls is $20.75.