Adelivery costs $2.75 per mile plus an additional $35 delivery fee, such that a delivery of 40 miles costs $145. if c(m) represents the total cost of the delivery service, in dollars, based on m miles, which statement is true?

a) the y-intercept of the function is 35, and the slope of the function is 2.75

b) the y-intercept of the function is 35, and the slope of the function is 3.625

c) the y-intercept of the function is 40, and the slope of the function is 2.75

d) the y-intercept of the function is 40, and the slope of the function is 3.625

The y-intercept of the function is 35, and the slope of the function

is 2.75 ⇒ answer A

Step-by-step explanation:

- A delivery costs $2.75 per mile plus an additional $35 delivery fee

- The delivery of 40 miles costs $145

- C(m) represents the total cost of the delivery service, in dollars, based

  on m miles

- We need to know, which statement is true

∵ The number of miles is m

∵ The cost per mile is $2.75

∵ The additional delivery fee is $35

∵ c(m) represents the total cost of the delivery service

∴ c(m) = 2.75 m + 35

- If m = 40 , then c(m) = 145 lets check that

- Substitute m in the function by 40

∵ c(m) = 2.75 × 40 + 35

∴ c(m) = 110 + 35 = 145

∴ c(m) = 2.75 m + 35 is a correct function

- The form of a linear function is f(x) = mx + c, where m is the slope of

  the function and c is the y-intercept

∵ c(m) = 2.75 m + 35

∴ c(m) represents a linear function which has slope 2.75 and

   y-intercept 35

* The true statement is :

The y-intercept of the function is 35, and the slope of the

function is 2.75

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.