Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect and additional 25 pounds each week. Write the equation for the total pounds,P, of aluminum cans after W weeks. What does the slope and y-intercet represent? How long will it take Rufus to collect 400 pounds of aluminum cans?

Answer:Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.The time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.Step-by-step explanation:It is given that Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect and additional 25 pounds each week. It means initial weight of cans = 100 poundsAdditional weight of cans = 25 pounds each weekLet W be the number of week.The equation for the total pounds P of aluminum cans after W weeks is[tex]P=100+25W[/tex]           .... (1)The slope intercept form of a line is[tex]y=mx+b[/tex]              .... (2)where, m is slope and b is y-intercept.From (1) and (2) we get[tex]m=25,b=100[/tex]It means slope and y-intercept are 25 and 100 respectively.Slope represents that the weight of can increased by 25 pounds each week. Y-intercept represents initial weight of cans, i.e., 100 pounds.We need to find the time taken by Rufus to collect 400 pounds of aluminum cans.Substitute P =400 in equation (1).[tex]400=100+25W[/tex]Subtract 100 from both sides.[tex]400-100=25W[/tex][tex]300=25W[/tex]Divide both sides by 25.[tex]12=W[/tex]Therefore, the time taken by Rufus to collect 400 pounds of aluminum cans is 12 weeks.