Okay, here we have this:
Considering the provided function and table, we are going to identify whether the table is correct or not, so we obtain the following:
So first we will solve for y in the equation and then we will evaluate the values of x one by one in the table:
5x – 2y = 8
– 2y = 8 - 5x
y = (8 - 5x)/-2
Now, let's evaluate the value of x:
x=-2:
y = (8 - 5x)/-2
y = (8 - 5(-2))/-2
y = (8 +10)/-2
y = (18)/-2
y = -9
x=-1:
y = (8 - 5x)/-2
y = (8 - 5(-1))/-2
y = (8 +5)/-2
y = (13)/-2
y = -6.5
x=0:
y = (8 - 5x)/-2
y = (8 - 5(0))/-2
y = (8 +0)/-2
y = (8)/-2
y = -4
x=1:
y = (8 - 5x)/-2
y = (8 - 5(1))/-2
y = (8 -5)/-2
y = (3)/-2
y = -1.5
x=2:
y = (8 - 5x)/-2
y = (8 - 5(2))/-2
y = (8 -10)/-2
y = (-2)/-2
y = 1
Finally we obtain that since when evaluating all the values of the function the outputs are the same as those of the tables, then Alice is correct.
