Suppose that the cost of a truck rental is related to the number of hours the truck is rented by a linear equation. Also, suppose the cost of a 2-hour rental is $55 and the cost of a 3-hour rental is $65. Find the cost of a 6-hour rental.: *
c = m h + b
55 = m (2) + b
65 = m (3) + b
------------------subtract
-10 = -m
m = 10
c = 10 h + b
55 = 20 + b
b = 35
so
c = 10 h + 35
if h = 6
c = 60 + 35 = 95
55 + (10 * 4) = ?
To find the cost of a 6-hour rental, we can use the given information to determine the equation that relates the cost to the number of hours.
Let's first define some variables:
Let x be the number of hours the truck is rented.
Let y be the cost of the truck rental.
We're given two data points: (2, 55) and (3, 65).
This means that when x = 2, y = 55, and when x = 3, y = 65.
We can use the formula for the equation of a line, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
To find the slope of the line, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the values (2, 55) and (3, 65) into the formula:
m = (65 - 55) / (3 - 2) = 10 / 1 = 10
So the slope of the line is 10.
Now, we need to find the value of the y-intercept, b. We can use one of the data points and substitute the values into the equation y = mx + b.
Let's use the point (2, 55):
55 = (10 * 2) + b
55 = 20 + b
b = 55 - 20
b = 35
So the y-intercept, b, is 35.
Now that we have the slope, m, and the y-intercept, b, we can determine the linear equation relating the cost of the rental to the number of hours:
y = 10x + 35
To find the cost of a 6-hour rental, substitute x = 6 into the equation:
y = 10 * 6 + 35
y = 60 + 35
y = 95
Therefore, the cost of a 6-hour rental is $95.