Question

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

Answer 1

Answer:

$n = \frac{4}{3}c$

$c:0\ \ \ \frac{3}{4}\ \ \ \frac{3}{2}\ \ \ \frac{9}{4}\ \ \ 3\ \ \ 3\frac{3}{4}\\n:0\ \ \ \ 1\ \ \ 2\ \ \ 3\ \ \ \ 4\ \ \ \ 5$

Step-by-step 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:

$(c_1,n_1) = (\frac{3}{4},1)$

$(c_2,n_2) = (3\frac{3}{4},5)$

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

$m = \frac{n_2 - n_1}{c_2 - c_1}$

$m = \frac{5-1}{3\frac{3}{4} - \frac{3}{4}}$

$m = \frac{4}{3}$

So: the equation is:

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

This gives:

$n = \frac{4}{3}(c - \frac{3}{4}) + 1$

$n = \frac{4}{3}c - 1 + 1$

$n = \frac{4}{3}c$

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

To complete the table

When $n = 2$

Substitute $n = 2$ in: $n = \frac{4}{3}c$

$2 = \frac{4}{3}c$

Make c the subject

$c = \frac{3*2}{4}$

$c = \frac{3}{2}$

When $n = 3$

Substitute $n = 3$ in: $n = \frac{4}{3}c$

$3 = \frac{4}{3} * c$

Make c the subject

$c = \frac{3*3}{4}$

$c = \frac{9}{4}$

When $c=3$

Substitute $c=3$ in: $n = \frac{4}{3}c$

$n = \frac{4}{3} * 3$

$n = 4$

So, the complete table is:

$c:0\ \ \ \frac{3}{4}\ \ \ \frac{3}{2}\ \ \ \frac{9}{4}\ \ \ 3\ \ \ 3\frac{3}{4}\\n:0\ \ \ \ 1\ \ \ 2\ \ \ 3\ \ \ \ 4\ \ \ \ 5$