Math

Question Which equation is nonlinear? y=x24y=x^{2}-4 or 3y5x=113y-5x=11?

Studdy Solution

STEP 1

Assumptions
1. We are given four different equations.
2. We need to identify which of these equations is nonlinear.
3. A nonlinear equation is one that does not graph as a straight line, which typically means it has exponents other than 1, coefficients that are not constant, or involves products of variables.

STEP 2

Analyze the first equation.
y=x24y = x^{2} - 4
This equation has an exponent of 2 on the variable xx, which means it is a quadratic equation and will graph as a parabola, not a straight line.

STEP 3

Analyze the second equation.
x=yx = y
This equation is linear because it can be rewritten as y=xy = x which is a first-degree polynomial, meaning it will graph as a straight line.

STEP 4

Analyze the third equation.
3y5x=113y - 5x = 11
This equation is linear because it can be rearranged to the form y=mx+by = mx + b where mm and bb are constants, which means it will graph as a straight line.

STEP 5

Analyze the fourth equation.
x=5x = 5
This equation is linear because it represents a vertical line where xx is always 5, regardless of the value of yy.

STEP 6

Identify the nonlinear equation.
From the analysis in the previous steps, we can see that the first equation, y=x24y = x^{2} - 4, is the only nonlinear equation among the given choices.
The nonlinear equation is y=x24y = x^{2} - 4.

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