When making a telephone call using a calling card, a call lasting 44 minutes cost $1.151.15. A call lasting 1313 minutes cost $2.952.95. Let y be the cost of making a call lasting x minutes using a calling card. Write a linear equation that models the cost of a making a call lasting x minutes.
You have two points: (44,1151.15) and (1313,2952.95)
Find the slope m of the line joining those two points, and your equation is easy to find, using either of the two points:
y-1151.15 = m(x-44)
or
y-2952.95 = m(x-1313)
To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we need to find the equation of a straight line that passes through two given points.
Let's consider the two data points given in the problem:
Point 1: (44, $1.15)
Point 2: (13, $2.95)
The equation of a straight line can be written in the form: y = mx + b, where y is the dependent variable (cost), x is the independent variable (minutes), m is the slope, and b is the y-intercept.
To find the equation, we need to determine the slope (m) and the y-intercept (b) using the given points.
Step 1: Calculate the slope (m)
The formula for calculating the slope (m) between two points (x₁, y₁) and (x₂, y₂) is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points given:
m = ($2.95 - $1.15) / (13 - 44)
m = $1.80 / (-31)
m ≈ -0.058
Step 2: Calculate the y-intercept (b)
To find the y-intercept (b), we can substitute one of the points (x, y) into the equation y = mx + b and solve for b.
Using the point (44, $1.15):
$1.15 = (-0.058 * 44) + b
$1.15 = -2.552 + b
b ≈ $3.702
Step 3: Write the linear equation
Now that we have the slope (m) and the y-intercept (b), we can write the equation of the line y = mx + b.
Putting the values into the equation:
y = -0.058x + $3.702
Therefore, the linear equation that models the cost of making a call lasting x minutes using a calling card is:
y = -0.058x + $3.702