Question
How to find parametric equations for the line y = 4x + 2
Answers
GPT-4o mini
To find parametric equations for the line given by \( y = 4x + 2 \), we can express both \( x \) and \( y \) in terms of a parameter, usually denoted as \( t \).
A simple way to do this is to let \( x \) be equal to the parameter \( t \). So we set:
\[
x = t
\]
Next, we can substitute this value of \( x \) into the equation of the line to find \( y \):
\[
y = 4x + 2 = 4t + 2
\]
Thus, we have the parametric equations for the line:
\[
\begin{align*}
x(t) &= t \\
y(t) &= 4t + 2
\end{align*}
\]
These parametric equations represent the same line defined by \( y = 4x + 2 \), and you can choose any parameterization by letting \( t \) take any range of values you desire. In this case, \( t \) can be any real number.
So, the final parametric equations for the line are:
\[
\begin{align*}
x &= t \\
y &= 4t + 2
\end{align*}
\]
where \( t \in \mathbb{R} \).
A simple way to do this is to let \( x \) be equal to the parameter \( t \). So we set:
\[
x = t
\]
Next, we can substitute this value of \( x \) into the equation of the line to find \( y \):
\[
y = 4x + 2 = 4t + 2
\]
Thus, we have the parametric equations for the line:
\[
\begin{align*}
x(t) &= t \\
y(t) &= 4t + 2
\end{align*}
\]
These parametric equations represent the same line defined by \( y = 4x + 2 \), and you can choose any parameterization by letting \( t \) take any range of values you desire. In this case, \( t \) can be any real number.
So, the final parametric equations for the line are:
\[
\begin{align*}
x &= t \\
y &= 4t + 2
\end{align*}
\]
where \( t \in \mathbb{R} \).