Question

Bob and Carl each renter the same kind of moving truck from ez move. There was a flat rental fee plus charge per mile that the truck was driven. Bob cost for his truck was $112.96 for 138 miles. Carl’s cost for his truck was $142.78
for 209 miles. Which equation can be used to represent the cost of the rental truck

Answer 1

It's a linear function: y = mx + b

We have (138; 112.96); (209; 142.78)

substitute the values of x and y to the formula of slope m:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{142.78-112.96}{209-138}=0.42$

Now we have: $y=0.42x+b$

We must find b. Substitute the value of x and y from first pair of numbers:

$112.96=0.42\cdot138+b\\\\112.96=57.96+b\ \ \ |-57.96\\\\b=55$

Answer: y = 0.42x + 55

Answer 2

Answer:

y = 0.42x + 55

Step-by-step explanation:

Let the equation for the cost of the truck be represented by y = mx + b,

where y = cost of truck per mile, x = number of miles, m = charge of the truck per mile and b = rental fee.

We are given that,

Cost for Bob's truck ( y ) = $112.96 for x = 138 miles, and

Cost for Carl's truck ( y ) = $142.78 for x = 209 miles.

This gives us the equations,

142.78 = 209m + b

112.96 = 138m + b

Subtracting these equations, we get,

29.82 = 71m

i.e. m = 0.42

Substituting the value of ' m ' in first equation, we get,

142.78 = 209 × 0.42 + b

i.e. 142.78 = 87.78 + b

i.e. b = 55.

Hence, the equation for the cost of the truck is y = 0.42x + 55