we are given
[tex]y=19.75x[/tex]
Here,
y is the number of gallons of water in the pool
x is the number of minutes the truck has been filing the pool
now, we will verify each options
option-A:
When x=1
then y=19.75
so, for 1 minute , number gallons =19.75
so, this is FALSE
option-B:
Since, we have
[tex]y=19.75x[/tex]
It is similar to equation of line
y=mx+b
But b=0
It means that it passes through origin
so, this is TRUE
option-C:
[tex]y=19.75x[/tex]
we can compare it with
y=mx
where m is the rate
so, we get
[tex]m=19.75[/tex]
while we are given
the water in swimming pool increase about 100 gallons by every 5 minutes
so, we get rate as
[tex]m=\frac{100}{5} =20[/tex] gallons per minute
this is close to 19.75
so, they are approximately equal
so, this is TRUE
option-d:
x-value and y-value will show relationship
and ratio will always be constant or equivalent
because it has linear relationship
so, this is TRUE
option-e:
We need to check
(8,150) ..so, x=8 and y=150
we can plug this in our equation
and we get
[tex]150=19.75\times 8[/tex]
[tex]150=158[/tex]
Since, left side is not equal to right side
so, this can not be point
so, this is FALSE
