Question

A water truck is filling a swimming pool. The equation that represents this relationship is y = 18.25x where y is the number of gallons of water in the pool and x is the number of minutes the truck has been filling the pool. Select True or False for each statement.the unit rate for this relationship is 1 gallon per 18.25 minutesO TrueO Falsethis is a proportional relationship because the graph of the equation is a straight line through the orginO TrueO Falsethe water in the swimming pool increases about 33 gallons every 10 minutesO TrueO Falsea table of related x- and y- values for this relationship would show equivalent ratiosO TrueO Falsethe point (12, 219) could be a point on this graphO TrueO False

Answer 1

Given the equation :

`y=18.25x`

Where : y is the number of gallons of water in the pool

and : x is the number of minutes the truck has been filling the pool.

1) the unit rate for this relationship is 1 gallon per 18.25 minutes ( false )

Because 18.25 represents the number of gallons per minute

2) this is a proportional relationship because the graph of the equation is a straight line through the origin ( True )

Because: when x = 0 , y = 0

3) the water in the swimming pool increases about 33 gallons every 10 minutes ( false )

Because after 10 minutes mean x = 10

so, when x = 10 , y = 18.25 * 10 = 182.5 gallons

4) a table of related x- and y- values for this relationship would show equivalent ratios (true)

Because : the ratios between the values will be y/x = 18.25 = constant

5) the point (12, 219) could be a point on this graph ( true )

Because : When x = 12 minutes , y = 18.25 * 12 = 219 gallons