Question

5. Select ALL of the following expressions that are linear functions (they do not need to be in slope-intercept form).

Answer 1

Answer:

The following are the LINEAR functions.

• $2x\:+\:4\:=\:3x\:-\:8$

• $y = 3x - 2$

• $1$

• $3x\:+\:-y\:=\:24$

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

$f(x)=mx+b$

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) $y^2=\:5x\:+2$

$y^2=\:5x\:+2$  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) $2x\:+\:4\:=\:3x\:-\:8$

$2x\:+\:4\:=\:3x\:-\:8$

$x=12$

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) $y = 3x - 2$

$y = 3x - 2$ is a linear function because it is of the form $f(x)=mx+b$ and the power of its x and y variables is 1. Hence, the function has a straight line graph.

4) $y\:+\:x^2\:=\:12$

$y\:+\:x^2\:=\:12$ 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) $y\:=\:x^2\:+\:2x$

$y\:=\:x^2\:+\:2x$ 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) $1$

$1$ is a constant function and a constant function is also considered linear in this context, as it is a polynomial of degree $0$ or is the $0$ polynomial.

7) $3x\:+\:-y\:=\:24$

$3x\:+\:-y\:=\:24$ 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.

• $2x\:+\:4\:=\:3x\:-\:8$

• $y = 3x - 2$

• $1$

• $3x\:+\:-y\:=\:24$