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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?

Verified Answer :

meerkat18

We are given with two conditions: after 1 hours, Estelle has 2 bags of leaves and after 3 hours, she has 6 bags of leaves. We translate these into points, we have (1,2) and (3,6). we get the slope of the points (4/2) or 2. we plug to the equation y-y1 = m (x-x1) where m is equal to 2. y-2 = 2 (x-1). Simplifiying, we get y -2 = 2x -2 or equal to y = 2x.

The problem states two given conditions:

One is that after 1 hour, Estelle has two bags of leaves and
after three hours she has 6 bags of leaves.

The equation of a line is y=mx + b where m is the slope and b
is the y-intercept of the line graph

Plotting the two points to get the m and b:

(1, 2) and (3, 6)

2=m1 + b ; b= 2-m    eqn
1

6=m3 +b        eqn 2

Solving for m and b can be done using systems of linear
equations or by substituting equation 1 to equation 2.

m=2 and b=0

So the equation of the line in the graph is y=2x

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