Question

Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and
16 minutes to lay down 44 cubic yards of mulch.
Plot five data points and the line that represent this direct variation relationship.​

Answer 1

Answer with explanation:

Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and  16 minutes to lay down 44 cubic yards of mulch.

Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.

Let k be the constant of proportionality, such that

$k=\dfrac{y}{x}$

For x= 4 and k= 11, $k=\dfrac{11}{4}$

Required equation: $y=\dfrac{11}{4}x$                        

Two points are given in question: (4,11) , (16,44).

Take x= 8 , $y=\dfrac{11}{4}(8)=22$i.e. point (8,22)

Similarly, for x= 12, y=33 i.e. point (12, 33)

For x= 20 , y= 55 i.e. point (20,55)

Five data points: (4,11) , (16,44), (8,22),  (12, 33), (20,55).

Now, we plot these points on graph and join them

Answer 2

Answer:

Here

Step-by-step explanation: