Answer:
The following are the LINEAR functions.
- [tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
- [tex]3x\:+\:-y\:=\:24[/tex]
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
[tex]f(x)=mx+b[/tex]
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) [tex]y^2=\:5x\:+2[/tex]
[tex]y^2=\:5x\:+2[/tex] 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) [tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
[tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
[tex]x=12[/tex]
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) [tex]y = 3x - 2[/tex]
[tex]y = 3x - 2[/tex] is a linear function because it is of the form [tex]f(x)=mx+b[/tex] and the power of its x and y variables is 1. Hence, the function has a straight line graph.
4) [tex]y\:+\:x^2\:=\:12[/tex]
[tex]y\:+\:x^2\:=\:12[/tex] 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) [tex]y\:=\:x^2\:+\:2x[/tex]
[tex]y\:=\:x^2\:+\:2x[/tex] 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) [tex]1[/tex]
[tex]1[/tex] is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree [tex]0[/tex] or is the [tex]0[/tex] polynomial.
7) [tex]3x\:+\:-y\:=\:24[/tex]
[tex]3x\:+\:-y\:=\:24[/tex] 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.
- [tex]2x\:+\:4\:=\:3x\:-\:8[/tex]
- [tex]3x\:+\:-y\:=\:24[/tex]
