Hector family is on a car trip when they are 84 miles from home hector begins recording the distance

the complete question in the attached figure

 A)  The points in the table are

(0,84) (1,146) (2,208) (3,270)

 m=(y2-y1)/(x2-x1)-------> m=(146-84)/(1-0)=62/1=62

84=62*0+b-------------- > b=84

Then

 y=62x+84

the answer to the question A is y=62x+84

 B)  Equation of remaining gasoline is g=16-(1/20)*d

a)   For d=100 miles

g=16-(1/20)*100=11 gallons

b)   For d=200 miles

g=16-(1/20)*200=6 gallons

c)    For d=300 miles

g=16-(1/20)*300=1 gallons

 C)   Using a graphic tool ----------- > view the graphic in file attached

g=16-(1/20)*d

 D)  Explain why the slope of the drawn line  in part C must be negative

The slope is negative because as the car advances gasoline is consumed to the point (320.0)

When the gasoline is zero  (g=0)  the car has traveled 320 miles

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step-by-step explanation:

i hope this : )