MATH SOLVE

2 months ago

Q:
# Hannah charges an hourly babysitting fee of $6 for two children, $7 for three children, and $8 for four or ﬁve children.Which is true about the table when c = the number of children and f = the fee per hour?c 1 2 3 4 5f 6 6 7 8 8A.The relationship is not linear between c and f.B.The relationship is linear between c and f.C.The relationship is not linear for c and linear for f.D.The relationship is linear for c but not f.

Accepted Solution

A:

A.The relationship is not linear between c and f.
A relationship is linear if and only if the ratio between changes in the dependent and independent variables is constant. So let's look at the data points we have.
c=2, f = 6; Not enough data yet to make a determination.
c=3, f = 7; We can now see a change in the children by 1 and a change in fee by 1. But with only 2 data points, that's still not enough.
c=4, f = 8; Another change of 1 in the children and a change in fee by 1. With just these three data points, the relationship looks linear with a change in children exactly matched by a 1:1 ratio with a change in fee.
c=5, f = 8; And here the linear relationship breaks down. If doesn't matter if the curve is linear during some small segment. The instant there's a segment that's not linear, the relationship is not linear. So with that in mind, let's look at the options.
A.The relationship is not linear between c and f.
* This is a true statement and the correct choice.
B.The relationship is linear between c and f.
* This is the exact opposite of A and therefore false. So it's a bad choice.
C.The relationship is not linear for c and linear for f.
* You can't claim this. It's a RELATIONSHIP between 2 variables. It's not a self relationship for each variable independently. So this is a bad choice.
D.The relationship is linear for c but not f.
* The same problem that applied for C above applies here. So bad choice.