Question

kanna wrote the function $d(x) = \frac{1}{2}x$ to determine the wheel distance for a truck length of $x$.
a. discuss: what does $d(x) = \frac{1}{2}x$ mean?
b. what is the value of $d(7)$ ?

Explanation:

Part a

The function \( d(x)=\frac{1}{2}x \) means that the wheel distance (\( d(x) \)) of the truck is half of the truck's length (\( x \)). In other words, to find the wheel distance, we multiply the truck's length by \( \frac{1}{2} \).

Step1: Substitute \( x = 7 \) into the function \( d(x)=\frac{1}{2}x \)

We know that the function is \( d(x)=\frac{1}{2}x \), and we need to find \( d(7) \). So we replace \( x \) with \( 7 \) in the function.
\( d(7)=\frac{1}{2}\times7 \)

Step2: Calculate the value

\( \frac{1}{2}\times7=\frac{7}{2} = 3.5 \)

Answer:

The wheel distance \( d(x) \) is half of the truck length \( x \), i.e., \( d(x)=\frac{1}{2}x \) implies \( d(x) \) is proportional to \( x \) with a constant of proportionality \( \frac{1}{2} \), meaning the wheel distance is half the truck's length.

Part b