Question

A driver wants to gauge the fuel efficiency of
her vehicle at speeds of 30 mph and above.
She notices that traveling at an average speed
of 40 mph results in a rating of 25 mpg,
whereas, at an average speed of 45 mph, her
car rates 15 mpg. Find an equation to model
the gas mileage, m, as a function of average
speed s mph.

Answer 1

Answer: Y = -2X + 105

Step-by-step explanation: let speed = x and mpg = y

Using linear equation

Y = MX +c

M = dy/dt = (15 - 25)/( 40 - 45) =

-10/5 = -2

When y = 15 , x = 45

15 = -2(45) + c

15 = -90 + c

C = 105

The model linear equation will be

Y = -2X + 105

Answer 2

Answer:

m = -2s + 105 for s > 30

Step-by-step explanation:

To get the gas mileage (m) as a function of average  speed (s) mph. If  m is for the fuel efficiency and s is for the average speed, it can be represented by the equation of a straight line.

(s₁, m₁) = (40, 25) and (s₂, m₂) = (45, 15)

The equation is given by:

$\frac{m-m_1}{s-s_1} =\frac{m_2-m_1}{s_2-s_1}$

Substituting values:

$\frac{m-25}{s-40} =\frac{15-25}{45-40}$

$\frac{m-25}{s-40} =-2$

$m-25 =-2(s-40)\\m-25=-2s+80\\m = -2s+105$

m = -2s + 105 for s > 30

m is in mpg and s is in mph