MATH SOLVE

2 months ago

Q:
# Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives.Number of Hours vs. Amount Left in TankNumber of Hours Spent Driving (h)3579Amount of Gas Left in Tank, in gallons (g)12840Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank?

Accepted Solution

A:

Number of Hours Amount of Gas

Spent Driving Left in Tank,

(h) in gallons (g)

h1=3 g1=12

h2=5 g2=8

h3=7 g3=4

h4=9 g4=0

h2-h1=5-3=2 g2-g1=8-12=-4

h3-h2=7-5=2 g3-g2=4-8=-4

h4-h3=9-7=2 g4-g3=0-4=-4

The equation that models the amount of gas left in the car as phan drives is a linear equation:

g-g1=m(h-h1)

Amount of gas left in the car: g

Number of hours spent driving: h

m=(g2-g1)/(h2-h1)

m=(8-12)/(5-3)

m=(-4)/(2)

m=-2

g-g1=m(h-h1)

g-12=(-2)(h-3)

g-12=(-2)(h)+(-2)(-3)

g-12=-2h+6

g-12+12=-2h+6+12

g=-2h+18

Answer: The equation models the amount of gas left in the car as Phan drives is: g=-2h+18

How many gallons of gasoline does it take to fill her tank?

This is when h=0

h=0→g=-2(0)+18→g=-0+18→g=18

Answer: It takes 18 gallons of gasoline to fill her tank

Spent Driving Left in Tank,

(h) in gallons (g)

h1=3 g1=12

h2=5 g2=8

h3=7 g3=4

h4=9 g4=0

h2-h1=5-3=2 g2-g1=8-12=-4

h3-h2=7-5=2 g3-g2=4-8=-4

h4-h3=9-7=2 g4-g3=0-4=-4

The equation that models the amount of gas left in the car as phan drives is a linear equation:

g-g1=m(h-h1)

Amount of gas left in the car: g

Number of hours spent driving: h

m=(g2-g1)/(h2-h1)

m=(8-12)/(5-3)

m=(-4)/(2)

m=-2

g-g1=m(h-h1)

g-12=(-2)(h-3)

g-12=(-2)(h)+(-2)(-3)

g-12=-2h+6

g-12+12=-2h+6+12

g=-2h+18

Answer: The equation models the amount of gas left in the car as Phan drives is: g=-2h+18

How many gallons of gasoline does it take to fill her tank?

This is when h=0

h=0→g=-2(0)+18→g=-0+18→g=18

Answer: It takes 18 gallons of gasoline to fill her tank