Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Jan 31, 2024

Which equation is nonlinear? $y=x^{2}-4$ or $3y-5x=11$ ?

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

STEP 3

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

STEP 4

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

STEP 5

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

STEP 6

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

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