Question

1. here is a graph of the function. label the axes. label at least two points with input - output pairs.
2. to convert feet to yards, you multiply the number of feet by \\(\frac{1}{3}\\).

a. name the two quantities in this situation that are in a functional relationship. which did you choose to be the independent variable? what is the variable that depends on it?
b. write an equation that represents the function.
c. draw the graph of the function. label at least two points with input - output pairs.

Explanation:

a. The two quantities are the number of feet and the number of yards. The independent variable is the number of feet (since we start with this value to convert), and the dependent variable (which depends on the independent variable) is the number of yards.
b. Since yards are calculated by multiplying feet by $\frac{1}{3}$, we define variables for each quantity and write the equation.
c. We use the equation to find input-output pairs, label the axes with the variables, plot the points, and draw the line connecting them.

Answer:

a. The two quantities are number of feet and number of yards.
Independent variable: Number of feet
Dependent variable: Number of yards (depends on the number of feet)

b. Let $f$ = number of feet, $y$ = number of yards.
$y = \frac{1}{3}f$

c.

1. Label the horizontal (x) axis: "Number of Feet ($f$)", vertical (y) axis: "Number of Yards ($y$)"
2. Calculate two input-output pairs:

• When $f=3$, $y=\frac{1}{3}(3)=1$ → Point: $(3, 1)$
• When $f=6$, $y=\frac{1}{3}(6)=2$ → Point: $(6, 2)$

1. Plot these two points, draw a straight line through them starting at the origin $(0,0)$.