Suppose that a household's monthly water bill (in dollars) is a linear function of the amount of water the household uses (in hundreds of cubic feet, hcf). when graphed, the function gives a line with a slope of 1.35 . see the figure below. if the monthly cost for 16 hcf is $45.98 , what is the monthly cost for 19 hcf?

Hello Evelyn, you have forgotten/omitted to post the graph.
The least we need to know is if the graph passes through the origin.  If not, we need to know the y-intercept.
We'll try to work backwards to suit the question.
Given 16 HCF costs $45.98, with a slope of 1.35.  This means that the y-intercept is 45.98-16*1.35=24.38
This means that the cost function is
f(x)=1.35x+24.38  where x is the consumption in HCF.

For 19 HCF, the cost is
f(19)=1.35(19)+24.38=$50.03