Truck Rental Plus charges its customers based on a linear model. the table to the right depicts this data. they charge their customers $95 for using their truck for a total of 100 miles and $140 for using their truck for a total of 200 miles
To find the equation of the linear model, we need to determine the rate at which the cost increases per mile. Since the data given includes two points, we can use them to form two equations and solve for the unknowns.
Let's use the slope-intercept form of a linear equation, y = mx + b, where y represents the cost and x represents the number of miles.
From the given information, we have two points: (100, 95) and (200,140).
Using the first point, we can substitute the values into the equation:
95 = m * 100 + b ---(equation 1)
Using the second point, we can substitute the values into the equation:
140 = m * 200 + b ---(equation 2)
Now, we can solve these two equations simultaneously to find the values of m and b.
To eliminate b, we can subtract equation 1 from equation 2:
140 - 95 = m * 200 - m * 100 + b - b
45 = m * 100
m = 45 / 100
m = 0.45
Now, substitute the value of m back into equation 1 to find the value of b:
95 = 0.45 * 100 + b
95 = 45 + b
b = 95 - 45
b = 50
Therefore, the linear model is given by the equation:
y = 0.45x + 50
Using this equation, you can determine the cost (y) for any given number of miles (x) when renting from Truck Rental Plus.