Question

Which of the following is a linear function?

one over three x = y − 3
y = x3 + 2
y = 6x2
y = two over three x

Answer 1

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

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

`(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*2`

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 = (2)/(3)x`

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