Question

all in the balance
the photosynthesis equation states that
$6\\ co_2$ and $6\\ h_2o$ molecules combine to
form $1\\ c_6h_{12}o_6$ molecule and $6\\ o_2$ molecules.
for every 6 carbon dioxide molecules, the
reaction produces 1 glucose molecule.

1. sep use mathematics write an

equation using two variables to model how
many glucose molecules are produced by
$6\\ co_2$ molecules. use $x$ for the number of
glucose molecules and $y$ for the number
of $co_2$ molecules.

1. ccc scale, proportion, and quantity

calculate how many glucose molecules are
produced by 6, 12, 18, and 24 $co_2$ molecules.
plot these points on the graph. what is the
relationship between the two variables?
math toolbox
proportion relationship
chart with co₂ molecules on y - axis and c₆h₁₂o₆ molecules on x - axis, grid from (0,0) to (6,26)

Explanation:

Step1: Define variable relationship

From the given ratio: 6 $\text{CO}_2$ molecules produce 1 glucose molecule, so the number of glucose molecules $x$ is $\frac{1}{6}$ of the number of $\text{CO}_2$ molecules $y$.
$x = \frac{1}{6}y$

Step2: Calculate glucose for 6 $\text{CO}_2$

Substitute $y=6$ into the equation.
$x = \frac{1}{6} \times 6 = 1$

Step3: Calculate glucose for 12 $\text{CO}_2$

Substitute $y=12$ into the equation.
$x = \frac{1}{6} \times 12 = 2$

Step4: Calculate glucose for 18 $\text{CO}_2$

Substitute $y=18$ into the equation.
$x = \frac{1}{6} \times 18 = 3$

Step5: Calculate glucose for 24 $\text{CO}_2$

Substitute $y=24$ into the equation.
$x = \frac{1}{6} \times 24 = 4$

Step6: Identify variable relationship

The equation $x = \frac{1}{6}y$ shows a direct proportional relationship (as $y$ increases, $x$ increases by a constant factor of $\frac{1}{6}$).

Answer:

1. The equation modeling the relationship is $x = \frac{1}{6}y$
2. - 6 $\text{CO}_2$ molecules produce 1 glucose molecule

• 12 $\text{CO}_2$ molecules produce 2 glucose molecules
• 18 $\text{CO}_2$ molecules produce 3 glucose molecules
• 24 $\text{CO}_2$ molecules produce 4 glucose molecules
• The variables have a direct proportional relationship (the number of glucose molecules is always $\frac{1}{6}$ the number of $\text{CO}_2$ molecules)
• The points to plot are $(1, 6)$, $(2, 12)$, $(3, 18)$, $(4, 24)$ (with $x$ as glucose molecules, $y$ as $\text{CO}_2$ molecules)