On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

Answer:

After a quick online search, I've found that the complete question is:

a) Parker paid $4.50 for three pounds of gummy candy. Assuming each pound of gummy candy costs  the same amount, complete the table of values representing the cost of gummy candy in pounds.

Then we want to graph the points, and then comes our question:

c) On the same day, Parker’s friend, Peggy, was charged $5 for 1 1/2 lb. of gummy candy. Explain in terms of the graph why this must be a mistake.

So first, we know that this is a proportional relationship (each pound of candy costs the same)

And 0 pounds of candy should cost $0.

Then the relation between y (price) and x (number of lb) is:

y = k*lb

where k is the cost per lb.

Knowing that Parker paid $4.50 for three pounds of gummy candy, the relation is:

$4.50 = k*3lb

($4.50/3lb) = k = $1.50/lb

Then the linear relation is:

y = ($1.50/lb)*x

Now, in this question we can see that Parker's friend was charged $5 for ( 1 and 1/2) lb of candy.

If we replace those values in the equation, we get:

$5 = ($1.50/lb)*(1 + 1/2)lb = $2.25

This equation is false, then, in terms of the graph, the point ( (1 and 1/2)lb, $5) does not belong on the graph that you found in the previous points.

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