The numbers of bottles a machine fills is proportional to the number of minutes the machine operates.the machine fills to 250 bottles every 20 minutes. which of the following graphs correctly models this relationship?its not b that's all I know cause I got it wrong.

Accepted Solution

Answer:First graph.Step-by-step explanation:GivensThe machine fills 250 bottles every 20 minutes.The given information is the rate of change of the linear relation between variables. Such ratio is[tex]r=\frac{250 \ bottles}{20 \ minutes} =\frac{25}{2} bottles/min[/tex]Now, the starting point of such relation is [tex](0,0)[/tex], because 0 bottles are filled in 0 minutes.The, we use the point-slope form to find the equation that models the linear graph[tex]y-y_{1} =m(x-x_{1} })\\y-0=\frac{25}{2})x-0)\\ y=\frac{25x}{2}[/tex]So, according to this relation, when [tex]x=2[/tex], then [tex]y=25[/tex].Therefore, the first graph is the right answer, because it shows the points (2,25) which is part of the relation.