Question

How do you find five ordered pairs of \[y=4x+10\]?

Answer 1

Hint: First take five different values of ‘x’. Then put those values in the given equation to find the five corresponding values of ‘y’. The five sets of (x, y) values will be the required ordered pairs of the given equation.

Complete step by step solution:
Ordered pairs: These are the set of ‘x’ and ‘y’ coordinates, for which the equation gets satisfied.
Ordered pairs are denoted as (x, y)
To obtain five ordered pairs of the given equation, we have to take five different ‘x’ values and substitute into the equation for corresponding values of ‘y’.
Let the values of ‘x’ are $-1$, $-2$, 0, 1 and 2.
Putting x=$-1$ in \[y=4x+10\], we get
$\begin{align}
  & \Rightarrow y=4\times -1+10 \\
 & \Rightarrow y=-4+10 \\
 & \Rightarrow y=6 \\
\end{align}$
So, the ordered pair is ($-1$, 6)
Putting x=$-2$ in \[y=4x+10\], we get
$\begin{align}
  & \Rightarrow y=4\times \left( -2 \right)+10 \\
 & \Rightarrow y=-8+10 \\
 & \Rightarrow y=2 \\
\end{align}$
So, the ordered pair is ($-2$, 2)
Putting x=0 in \[y=4x+10\], we get
$\begin{align}
  & \Rightarrow y=4\times 0+10 \\
 & \Rightarrow y=0+10 \\
 & \Rightarrow y=10 \\
\end{align}$
So, the ordered pair is (0, 10)
Putting x=1 in \[y=4x+10\], we get
$\begin{align}
  & \Rightarrow y=4\times 1+10 \\
 & \Rightarrow y=4+10 \\
 & \Rightarrow y=14 \\
\end{align}$
So, the ordered pair is (1, 14)
Putting x=2 in \[y=4x+10\], we get
$\begin{align}
  & \Rightarrow y=4\times 2+10 \\
 & \Rightarrow y=8+10 \\
 & \Rightarrow y=18 \\
\end{align}$
So, the ordered pair is (2, 18)
These are the five required ordered pairs of the given equation.

Note:
Ordered pair helps to locate a point on the Cartesian plane for better visual comprehension and to get different sets of solutions for a given equation. The numeric values in an ordered pair can be integers or fractions.