When making a telephone call using a calling card, a call lasting 3 minutes cost $1.65. A call lasting 11 minutes cost $4.85. Let y ba the cost of making a call lasting x minutes using a calling card. Write a linerar equation that models the cost of making a call lasting x minutes.
The per-minute charge is $3.20/8 = 40 cents.
Assume there is an additional connection charge (A) and fit an equation of the form
Cost = A + 0.40 t
to the existing data. The cost will be in dollars and t must be in minutes.
To write a linear equation that models the cost of making a call lasting x minutes, let's consider the given information about two different calls.
Call 1: 3 minutes, cost $1.65
Call 2: 11 minutes, cost $4.85
We can use these two data points to determine the equation of the line that represents the cost of making a call lasting any given number of minutes.
Step 1: Identify two points on the line
Using the given information, we have two points: (3, 1.65) and (11, 4.85). The x-coordinate represents the minutes, and the y-coordinate represents the cost in dollars.
Step 2: Find the slope of the line
The slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Plugging in the values, we have:
m = (4.85 - 1.65) / (11 - 3)
= 3.20 / 8
= 0.40
Therefore, the slope of the line is 0.40.
Step 3: Use the slope-intercept form of a linear equation
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Step 4: Find the y-intercept
Using one of the points (3, 1.65) and the slope (0.40), we can substitute the values into the slope-intercept form to find the y-intercept.
1.65 = 0.40 * 3 + b
1.65 = 1.20 + b
b = 1.65 - 1.20
b = 0.45
Therefore, the y-intercept is 0.45.
Step 5: Write the linear equation
Using the slope (m = 0.40) and the y-intercept (b = 0.45), we can write the linear equation:
y = 0.40x + 0.45
Thus, the linear equation that models the cost of making a call lasting x minutes using a calling card is y = 0.40x + 0.45.