Answer:
You're looking for the graph [tex]y=2x[/tex]
Step-by-step explanation:
If Estelle is raking in leaves at a constant rate, which we usually assume for cases like this, we're looking for a function of the form
[tex]y=kx+m[/tex]
x here is going to be the number of hours, or time.
y is going to be the number of bags she has raked in.
First of all, we know that at time 0, she hasn't raked in any leaves. So when x is 0, we know y is 0. Let's put these values in our function.
[tex]0 = k * 0 + m[/tex]
[tex]0 = 0 + m[/tex]
[tex]m = 0[/tex]
We now know m is 0.
We also know that after 1 hour, Estelle has 2 bags of leaves. So when x is 1, y will be 2. Let's put these values in.
[tex]2 = k*1[/tex]
We're excluding m as we know it's 0.
[tex]k=2[/tex]
So k is 2, and m is 0. Let's put these values in our original function [tex]y=kx+m[/tex]:
[tex]y = 2x + 0[/tex]
[tex]y=2x[/tex]
The equation is y=2x.
Putting this into a graphing calculator, we get this graph (attached).
