Question

will some one plz help



Find the constant of proportionality and the unit rate for the data in the table. Then write an equation to represent the relationship between time t and distance d

Answer 1

" constant of proportionality" also known as "constant of variation"
so we know that "time" is "directly proportional", or "varies directly" with "distance

so \(\begin{array}{cccllll}
\textit{something }&\textit{varies directly to }&\textit{something else}\\ \quad \\
\textit{something }&={\color{red}{ \textit{some value }}}&\textit{something else}\\ \quad \\
y&={\color{red}{ n}}&x&\implies y={\color{red}{ n}}x
\end{array}\\ \quad \\

\begin{array}{llll}
x\qquad &y\\
\hline\\
2&90\\
3&135\\
5&225\\
6&270
\end{array}\qquad
\begin{array}{llll}
\textit{when x=2, y=90}\implies y={\color{red}{ n}}x\implies 90={\color{red}{ n}}(2)
\\ \quad \\
\textit{what's the value for "n"?}
\end{array}\)

Answer 2

anyhow, "n" would be your " constant of proportionality" also known as "constant of variation"

once you find "n"
plug its value in y = nx
and that'd be the equation