Answer:
The following are the LINEAR functions.
Step-by-step explanation:
We know that linear functions are the equations with a straight line graph in an XY plane.
Also, a linear function is a function of the form
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
where m is the slope and b is the y-intercept. The only power of the variable is 1.
So, from the given expressions we can determine that:
1) ![y^2=\:5x\:+2](https://tex.z-dn.net/?f=y%5E2%3D%5C%3A5x%5C%3A%2B2)
is NOT a linear function because the power of y is 2, hence the graph won't be a straight line. Therefore, it is not a linear function
2) ![2x\:+\:4\:=\:3x\:-\:8](https://tex.z-dn.net/?f=2x%5C%3A%2B%5C%3A4%5C%3A%3D%5C%3A3x%5C%3A-%5C%3A8)
![2x\:+\:4\:=\:3x\:-\:8](https://tex.z-dn.net/?f=2x%5C%3A%2B%5C%3A4%5C%3A%3D%5C%3A3x%5C%3A-%5C%3A8)
![x=12](https://tex.z-dn.net/?f=x%3D12)
This is a linear equation is an equation of a straight line, written in one variable. The only power of the variable is 1
3) ![y = 3x - 2](https://tex.z-dn.net/?f=y%20%3D%203x%20-%202)
is a linear function because it is of the form
and the power of its x and y variables is 1. Hence, the function has a straight line graph.
4) ![y\:+\:x^2\:=\:12](https://tex.z-dn.net/?f=y%5C%3A%2B%5C%3Ax%5E2%5C%3A%3D%5C%3A12)
is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.
5) ![y\:=\:x^2\:+\:2x](https://tex.z-dn.net/?f=y%5C%3A%3D%5C%3Ax%5E2%5C%3A%2B%5C%3A2x)
is NOT a linear function because the power of x is 2, hence the graph won't be a straight line. Therefore, it is not a linear function.
6) ![1](https://tex.z-dn.net/?f=1)
is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree
or is the
polynomial.
7) ![3x\:+\:-y\:=\:24](https://tex.z-dn.net/?f=3x%5C%3A%2B%5C%3A-y%5C%3A%3D%5C%3A24)
is a linear function as the power of its x and y variables is 1. Hence, the function has a straight line graph. Therefore, it is a linear function.
In a summary, the following are the LINEAR functions.