Question

Josie is making pizza dough. Complete the double number line by filling in the missing values

Answer 1

`n = (4)/(3)c`

`c:0\ \ \ (3)/(4)\ \ \ (3)/(2)\ \ \ (9)/(4)\ \ \ 3\ \ \ 3(3)/(4)\\n:0\ \ \ \ 1\ \ \ 2\ \ \ 3\ \ \ \ 4\ \ \ \ 5`

Explanation:

Given

See attachment for complete question

Required

Complete the double number line

The given double number lines represent a linear function between cups of flour (c) and number of batched (n)

Pick any two pairs:

`(c_1,n_1) = ((3)/(4),1)`

`(c_2,n_2) = (3(3)/(4),5)`

First, calculate the rate of change (i.e. slope, m):

`m = (n_2 - n_1)/(c_2 - c_1)`

`m = (5-1)/(3(3)/(4) - (3)/(4))`

`m = (4)/(3)`

So: the equation is:

`n = m(c - c_1) + n_1`

This gives:

`n = (4)/(3)(c - (3)/(4)) + 1`

`n = (4)/(3)c - 1 + 1`

`n = (4)/(3)c`

So, the above represents the relationship between n and c.

To complete the table

When
`n = 2`

Substitute
`n = 2` in:
`n = (4)/(3)c`

`2 = (4)/(3)c`

Make c the subject

`c = (3*2)/(4)`

`c = (3)/(2)`

When
`n = 3`

Substitute
`n = 3` in:
`n = (4)/(3)c`

`3 = (4)/(3) * c`

Make c the subject

`c = (3*3)/(4)`

`c = (9)/(4)`

When
`c=3`

Substitute
`c=3` in:
`n = (4)/(3)c`

`n = (4)/(3) * 3`

`n = 4`

So, the complete table is:

`c:0\ \ \ (3)/(4)\ \ \ (3)/(2)\ \ \ (9)/(4)\ \ \ 3\ \ \ 3(3)/(4)\\n:0\ \ \ \ 1\ \ \ 2\ \ \ 3\ \ \ \ 4\ \ \ \ 5`