Question

which equation represents a linear function? equation 1: y = 2x2 1 equation 2: y2 = 3x 1 equation 3: y = 5x – 1 equation 4: y = 4x4 – 1 (5 points) equation 1 equation 2 equation 3 equation 4

Answer 1

Option -3 Equation 3 -
`y=5x-1`

Explanation:

Given : Equation 1 -
`y=2x^2+1`

Equation 2 -
`y^2=3x+1`

Equation 3 -
`y=5x-1`

Equation 4 -
`y=4x^4-1`

To find : Which equation represents a linear function?

Solution :

A linear function - It is in the form
`y = f(x) = a + bx`.

A linear function has one independent variable and one dependent variable.

A linear function is a polynomial of degree one or zero.

From the following equation only equation 3 is a linear function,because it has one independent variable -1 and one dependent variable y on x and a polynomial of degree 1.

Therefore, Equation 3 -
`y=5x-1` is a linear function.

Answer 2

The correct result would be equation 3: y = 5x - 1, because a linear function is a polynomial of degree one or zero. Therefore, equations 1, 2, and 4 can't be represented as a linear function, because they have the degree of 2 or more.