Question

Which of the following is a linear function?

Answer 1

Answer:

$\bold{y = 3x + 2}$

Step-by-step explanation:

In a linear equation, $y=mx+b$, the "$m$" is identified as the slope, while the b is where you begin, the coefficient: y-intercept.

Now, with that said, let us look at each option, and see which one matches the linear equation.

Option 1

One over three x = y - 3

$\frac{1}{3}x=y-3$

As you can see, the $y$ should be in front of the equation. And the $-3$ should be next to $x$.

Option 2

$y = 3x + 2$

This equation is a  linear equation: the $y$ is in the right place, the coefficient is right next to $x$, and where you begin is at the right place. If you look at this equation, and the linear equation, you will notice they both match.

Option 3

$y = 6\times2$

The equation does not make sense in terms of linear equations, first off all. There is nothing to show it is a linear equation, except from the $y$. It is the same thing as just adding two numbers and putting an equal sign and $y$ in front of it, which is not a linear equation.

Option 4

y = two over three x

$y = \frac{2}{3}x$

There is no coefficient in this equation, therefore, it is not a linear equation.