Question

Linear Function

X | f(x) = 2x + 5
1 | 7
2 | 9
3 | 11
4 | 13
5 | 15
6 | 17
Linear functions grow by equal differences over equal intervals. In the table above, what column could be added to prove this relationship?
A) Δx
B) Δy
C) Δx/y
D) Δy/x

Answer 1

B because x is the independent variable; you could choose any number for x

Answer 2

B) Δy

Explanation:

Where we analyse a linear function, we must consider variations of each variable.

Also, linear functions variate according to its constant ratio of change, which is defined as

`r=(\Delta y)/(\Delta x)`

Which is the variation of the vertical value, regarding x-values.

So, if we want to show this variation, we must include a colum
`\Delta y`, which shows the variation we need, because it's the dependent value, then we can analyse the variation of the function for a certain x-interval.

Therefore, the right answer is B.