Roberto is having his house painted. The job takes three days, and he pays the painter the same hourly rateevery day. The cost of the job is in the chart below.Hours workedAmount paidDay 15$300Day 24$240Day 36$360What is the painter's unit rate of change of dollars with respect to time; that is, how much is the painter paid forone hour worked?

Answer:[tex]\$60\ per\ hour[/tex]Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the originLetx -----> the number of hours workedy ----> the amount paid in dollarsIn this problem we have a proportional variation, between two variables, x, and yFind out the constant of proportionality kFor (5,300) -----> [tex]k=y/x[/tex] ----> [tex]k=300/5=60\ \$/h[/tex]For (4,240) -----> [tex]k=y/x[/tex] ----> [tex]k=240/4=60\ \$/h[/tex]For (6,360) -----> [tex]k=y/x[/tex] ----> [tex]k=360/6=60\ \$/h[/tex]The constant k is [tex]k=60\ \$/h[/tex]The equation is equal to[tex]y=60x[/tex]The unit rate of change of dollars with respect to time is equal to the constant of proportionality or slope of the linear equationtherefore[tex]\$60\ per\ hour[/tex]