Question

The constant rate of change of a function is -5. Describe the graph of the function as you look at it from left to right.

Does the table represent data with a constant rate of change? Justify your answer.

Answer 1

notice the table of values

when x = 2, y = -5

then "x" goes 2 units over to 4, and "y" moves over to 5, now from -5 to 5 is 10 units, so when "x" moved just 2 units, "y" went 10.

then "x" goes further down to 7, moving 3 units over,
and "y" goes further from 5 to 20? what the? it went 15 units.

so.... hmmm notice, is we do some quick splitting and instead check how much "y" is moving for every unit on "x".

notice, on 2 units of "x", "y" moved 10 units
and on 3 units of "x", "y" moved 15 units, like from 5 to 20.

so, "y" is really moving 5 units on every unit moved by "x", so the "rate of change" or slope is indeed constant, is 3 to 1 all the way.