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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 25 minutes of calls is $26.25, and the remaining credit after 51 minutes of calls is $22.35. What is the remaining credit after 65 minutes of calls?

User Masika
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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.
User Fny
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