Question

The table shows a linear function(will insert picture at the end).

a) Determine the difference of outputs of any two inputs that are one unit apart. Show your work.

b) Determine the difference of outputs of any two inputs that are two units apart. Show your work.

c) Determine the difference of outputs of any two inputs that are 3 units apart. Show your work.

d) What do you notice about the ratios of the differences in the outputs to the input intervals? Explain your answer.
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Answer 1

The function is linear. The difference in outputs will be 5a and 5b. Therefore, the ratio will be a/b

Explanation:

Answer 2

assuming you know about straight lines...

equation of the line :

`(y - 7) = (7 - 2)/(0 - ( - 1)) (x - 0)`

y=5x+7

a) let's take 0 and 1, (which is already given)

f(1)-f(0)

=>[ 5(1)+7]-[5(0)+7)]

=5

b) 2 and 0,

[5(2)+7]-[5(0)+7]

=10

ratio= 10/5=2

since the function is linear, i.e. the slope is constant, the difference in two values in successive in intervals depends only on the ratio of the size of interval

let's say we have intervals of size a and b

(as you can see the constant gets cancelled)

difference in outputs will be 5a and 5b respectively.

and hence, ratio will be a/b

hope this explains