Identifying Linear vs Nonlinear Functions

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They have a variable with a power greater than 1.

They are always written in the form y = mx + b.

Their graphs are straight lines.

They can have variables with negative powers.

y = mx^3 + b

y = mx + b^2

ax + by = c

y = mx^2 + b

Desmos

GeoGebra

GraphCalc

WolframAlpha

A straight line

A circle

A hyperbola

A parabola

A straight line

A hyperbola

A circle

A parabola

y = 3x + 2

y = 2x^3 + 1

y = -x + 1

y = 4x - 1

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Because it has a variable with a power of 1.

Because it is written in slope-intercept form.

Because it has a constant term.

Because the variable is in the denominator.

By checking if the equation has a constant term.

By checking if the variable is in the denominator.

By checking if the equation is written in slope-intercept form.

By checking if the variable has a power of 1.