Question

ever since tristan was a small child, his favorite food has always been carrots. he likes them so much he wants to plant a garden in his backyard just to grow carrots.
there is a proportional relationship between the size of tristan’s garden (in square feet), ( x ), and the number of carrots he can grow at a time, ( y ).
graph with x-axis labeled square feet from 0 to 20, y-axis labeled carrots from 0 to 20, and a line passing through the origin and (4, 20) (approximate)
write an equation for the relationship between ( x ) and ( y ). simplify any fractions.
( y = square )

Explanation:

Step1: Identify proportional form

Proportional relationships follow $y = kx$, where $k$ is the constant of proportionality.

Step2: Pick a point from the graph

Choose the point $(2, 10)$ (when $x=2$, $y=10$).

Step3: Solve for $k$

Substitute $x=2$, $y=10$ into $y=kx$:
$$10 = k \times 2$$
$$k = \frac{10}{2} = 5$$

Step4: Write the final equation

Substitute $k=5$ back into $y=kx$.

Answer:

$y = 5x$