Question

Estelle is raking leaves in her yard. After 1 hour, she has 2 bags of leaves. After 3 hours, she has 6 bags of leaves. Which graph represents Estelle's leaf raking progress? (2 points)

Answer 1

You're looking for the graph
`y=2x`

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

`y=kx+m`

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.

`0 = k * 0 + m`

`0 = 0 + m`

`m = 0`

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.

`2 = k*1`

We're excluding m as we know it's 0.

`k=2`

So k is 2, and m is 0. Let's put these values in our original function
`y=kx+m`:

`y = 2x + 0`

`y=2x`

The equation is y=2x.

Putting this into a graphing calculator, we get this graph (attached).