Question

Ryan is trying to determine whether 2.7x – 5.9 is equivalent to 2.8x – 5.9. To test this, he substitutes 0 for x into both expressions. Explain why this will not give him the correct answer.

Answer 1

Because 2.7*0 = 0  and 2.8*0 = 0

He needs to plug in some other value like x = 1

Answer 2

Each of the 2 expressions given is a linear function of the form y = mx + b.
These two fundtions have the same y-intercept:  -5.9, but the slopes of the two lines are different.  In both cases, f(0) = 0 - 5.9, but this does not indicate that 2.7x-5.9 = 2.8x-5.9 in general.

If Ryan were to subst. 1 for x in these two functions, the results would not be identical:  2.7(1) - 5.9 and 2.8(1) - 5.9.

Hope Ryan comes to realize that this test of his will not give him the correct answer.