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3 votes
Which equation is non-linear?

A)
y=3x^3-10
B)
y=1/2x+4
C)
y=4x-5/3
D)
-3x--7y=-21

2 Answers

4 votes

Answer:


\huge\boxed{\text{A is not linear.}}

Explanation:

Linear equations are equations that, when graphed, form a "line" and have a constant rate of change.

Usually, these are in the form
y=mx+b when put in that order.

There are a few types of equations, I'll list some of the major ones

  • Linear = has a constant rate of change
  • Exponential = increases for x as the exponent
  • Quadratic = is in a binomial, trinomial, or polynomial - it has a vertex

Linear functions are usually in the form
y=mx+b

Exponential functions are usually in the form
y=b^x

Quadratic functions are usually in the form
ax^2 + bx + c

We must note that linear functions can not

A) Have an exponent on any x term

B) Have x and y multiplied by each other

We can see that every equation, except A

A) Follows the form
y=mx+b (
-3x--7y=-21 can be simplified to
y= (3)/(7)x-3)

B) Does not have any exponents on their x terms

That leaves A) to be the equation that isn't linear.

Hope this helped!

User Nightfixed
by
7.4k points
4 votes

Answer:

Equation A is non-linear.

Explanation:

We are given four equations in which we need to determine if they are linear or non-linear relationships.

Firstly, we need to know some information about linear equations:

  • Linear equations cannot have an exponent.
  • Linear equations have a constant slope and are straight lines.
  • Linear equations can be negative or positive.
  • Linear equations have a domain of all real numbers. They also have a range of all real numbers.

Now, in order to check this easily, we need to place these equations into slope-intercept form.

Equation A


\displaystyle y = 3x^3 - 10

We see that this has an exponent, so this cannot be a linear equation.

In fact, because it is cubed, this is called a cubic function. Therefore, equation A is not a linear equation.

Equation B


\displaystyle y = (1)/(2)x + 4

This equation does not have a exponent. It also has a slope and a y-intercept. Therefore, equation B is a linear equation.

Equation C


\displaystyle y = 4x -(5)/(3)

The equation does not have a exponent. It also has a slope and a y-intercept. Therefore, equation C is a linear equation.

Equation D


-3x--7y = -21

First off, we need to get this equation into slope-intercept form, if possible.


\displaystyle -3x -- 7y = -21\\\\-3x + 7y = -21 \ \ \ \text{Change the sign on 7y.}\\\\7y = 3x - 21 \ \ \ \text{Move 3x to the other side by adding.}\\\\(7y)/(7)=(3x-21)/(7) \ \ \ \text{Divide both sides by 7 to isolate y.}\\\\\bold{y = (3)/(7)x-3}

Our final equation is
\displaystyle y = (3)/(7)x-3.

The equation does not have an exponent. It has a constant slope and a y-intercept. Therefore, equation D is a linear equation.

Let's check our equations:

  • Equation A:
    \displaystyle y = 3x^3 - 10 \ \text{X}
  • Equation B:
    \displaystyle y = (1)/(2)x + 4 \ \checkmark
  • Equation C:
    \displaystyle y = 4x -(5)/(3) \ \checkmark
  • Equation D:
    \displaystyle y = (3)/(7)x-3 \ \checkmark

Therefore, we have determined that Equation A is not a linear equation, making it non-linear.

User Rocket Ronnie
by
8.1k points

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