When making a phone call using calling card a call lasting 3 minutes costs $1.60. A call lasting 10 minutes costs $4.40. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that relates to the cost of making the call y, to the time x.
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To write a linear equation that relates the cost of making the call (y) to the time (x), we can use the given information about the cost of calls lasting 3 minutes and 10 minutes.
Let's determine the cost per minute for both of these calls:
For a 3-minute call costing $1.60, the cost per minute is $1.60 ÷ 3 = $0.53 (rounded to two decimal places).
For a 10-minute call costing $4.40, the cost per minute is $4.40 ÷ 10 = $0.44 (rounded to two decimal places).
Since we know that the cost per minute is decreasing from $0.53 to $0.44, we can assume that the equation will be of the form: y = mx + b, where m is the slope (cost per minute) and b is the y-intercept (initial cost).
Substituting the given values, we have two points: (3, 1.60) and (10, 4.40).
Using the slope formula (m = (y2 - y1) / (x2 - x1)), we can find the slope (m):
m = (4.40 - 1.60) / (10 - 3) = 2.80 / 7 = 0.40.
Now we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) is one of the given points. Let's use the point (3, 1.60):
y - 1.60 = 0.40(x - 3).
Expanding and rearranging the equation, we get:
y - 1.60 = 0.40x - 1.20,
y = 0.40x - 1.20 + 1.60,
y = 0.40x + 0.40.
Therefore, the linear equation that relates the cost of making the call (y) to the time (x) is:
y = 0.40x + 0.40.