Question

The following table shows a proportional relationship between m and n

Answer 1

m = 7 n ( the '=' is meant to be the proportional sign)

Explanation:

21 ÷ 3 = 7

35 ÷ 5 = 7

56 ÷ 8 = 7

Answer 2

`y=7x`

Explanation:

Notice that if you divide each n-value by its correspoding m-value, you always have 7 as a result, that means it's the constant ratio of change,

21/3 = 7

35/5 = 7

56/8 = 7

Now, this is a linear relatioship by definition, where its constant ratio is 7, but geometrically, that ratio is the slope of a linear equation.

So, we need to use the slope 7, one pair from the table and the point-slope formula

`y-y_(1) =m(x-x_(1) )\\y-21=7(x-3)\\y=7x-21+21\\y=7x`

Therefore, an equation that models the given table is

`y=7x`