The equation
is a function
Explanation:
Given that the graph contains the coordinates
,
,
and ![(2,6)](https://tex.z-dn.net/?f=%282%2C6%29)
We need to determine whether the equation
is a function.
To determine the equation is a function, let us substitute the coordinates in the equation and check whether it satisfies the equation.
Let us substitute the coordinate
in the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Thus, we have,
![0=2(-1)+2](https://tex.z-dn.net/?f=0%3D2%28-1%29%2B2)
![0=-2+2](https://tex.z-dn.net/?f=0%3D-2%2B2)
![0=0](https://tex.z-dn.net/?f=0%3D0)
Thus, the coordinate
satisfies the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Substituting the coordinate
in the equation, we have,
![2=2(0)+2](https://tex.z-dn.net/?f=2%3D2%280%29%2B2)
![2=2](https://tex.z-dn.net/?f=2%3D2)
Thus, the coordinate
satisfies the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Substituting the coordinate
in the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
![4=2(1)+2](https://tex.z-dn.net/?f=4%3D2%281%29%2B2)
![4=4](https://tex.z-dn.net/?f=4%3D4)
Thus, the coordinate
satisfies the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Substituting the coordinate
in the equation, we get,
![6=2(2)+2](https://tex.z-dn.net/?f=6%3D2%282%29%2B2)
![6=6](https://tex.z-dn.net/?f=6%3D6)
Thus, the coordinate
satisfies the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Hence, the coordinates
,
,
and
satisfies the equation ![y=2x+2](https://tex.z-dn.net/?f=y%3D2x%2B2)
Thus, the equation
is a function.