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x-2y=-6

Algebra Calculus Trigonometry Matrix

Question

x-2y=-6

Function

x=-6

Evaluate

x-2y=-6

\text{To find the }x\text{-intercept,set }y\text{=0}

x-2\times 0=-6

Any expression multiplied by 0 equals 0

x-0=-6

Solution

x=-6

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\text{Find the }x\text{-intercept/zero}

Find the y-intercept

Find the slope

Solve the equation

x=-6+2y

Evaluate

x-2y=-6

Solution

x=-6+2y

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\text{Solve for }x

\text{Solve for }y

Testing for symmetry

\textrm{Not symmetry with respect to the origin}

Evaluate

x-2y=-6

\text{To test if the graph of }x-2y=-6\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}

-x-2\left(-y\right)=-6

Evaluate

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Evaluate

-x-2\left(-y\right)

Multiply the numbers

-x-\left(-2y\right)

Rewrite the expression

-x+2y

-x+2y=-6

Solution

\textrm{Not symmetry with respect to the origin}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

r=-\frac{6}{\cos\left(\theta \right)-2\sin\left(\theta \right)}

Evaluate

x-2y=-6

\text{To convert the equation to polar coordinates,substitute }x\text{ for }r\cos\left(\theta \right)\text{ and }y\text{ for }r\sin\left(\theta \right)

\cos\left(\theta \right)\times r-2\sin\left(\theta \right)\times r=-6

Factor the expression

\left(\cos\left(\theta \right)-2\sin\left(\theta \right)\right)r=-6

Solution

r=-\frac{6}{\cos\left(\theta \right)-2\sin\left(\theta \right)}

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Rewrite in polar form

Rewrite in slope-intercept form

Find the first derivative

\frac{dy}{dx}=\frac{1}{2}

Calculate

x-2y=-6

Take the derivative of both sides

\frac{d}{dx}\left(x-2y\right)=\frac{d}{dx}\left(-6\right)

Calculate the derivative

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Evaluate

\frac{d}{dx}\left(x-2y\right)

Use differentiation rules

\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2y\right)

\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}

1+\frac{d}{dx}\left(-2y\right)

Evaluate the derivative

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Evaluate

\frac{d}{dx}\left(-2y\right)

Use differentiation rules

\frac{d}{dy}\left(-2y\right)\times \frac{dy}{dx}

Evaluate the derivative

-2\frac{dy}{dx}

1-2\frac{dy}{dx}

1-2\frac{dy}{dx}=\frac{d}{dx}\left(-6\right)

Calculate the derivative

1-2\frac{dy}{dx}=0

Move the constant to the right-hand side and change its sign

-2\frac{dy}{dx}=0-1

Removing 0 doesn't change the value,so remove it from the expression

-2\frac{dy}{dx}=-1

Change the signs on both sides of the equation

2\frac{dy}{dx}=1

Divide both sides

\frac{2\frac{dy}{dx}}{2}=\frac{1}{2}

Solution

\frac{dy}{dx}=\frac{1}{2}

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\text{Find the derivative with respect to }x

\text{Find the derivative with respect to }y

Find the second derivative

\frac{d^2y}{dx^2}=0

Calculate

x-2y=-6

Take the derivative of both sides

\frac{d}{dx}\left(x-2y\right)=\frac{d}{dx}\left(-6\right)

Calculate the derivative

More Steps Hide Steps

Evaluate

\frac{d}{dx}\left(x-2y\right)

Use differentiation rules

\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2y\right)

\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}

1+\frac{d}{dx}\left(-2y\right)

Evaluate the derivative

More Steps Hide Steps

Evaluate

\frac{d}{dx}\left(-2y\right)

Use differentiation rules

\frac{d}{dy}\left(-2y\right)\times \frac{dy}{dx}

Evaluate the derivative

-2\frac{dy}{dx}

1-2\frac{dy}{dx}

1-2\frac{dy}{dx}=\frac{d}{dx}\left(-6\right)

Calculate the derivative

1-2\frac{dy}{dx}=0

Move the constant to the right-hand side and change its sign

-2\frac{dy}{dx}=0-1

Removing 0 doesn't change the value,so remove it from the expression

-2\frac{dy}{dx}=-1

Change the signs on both sides of the equation

2\frac{dy}{dx}=1

Divide both sides

\frac{2\frac{dy}{dx}}{2}=\frac{1}{2}

Divide the numbers

\frac{dy}{dx}=\frac{1}{2}

Take the derivative of both sides

\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(\frac{1}{2}\right)

Calculate the derivative

\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{1}{2}\right)

Solution

\frac{d^2y}{dx^2}=0

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\text{Find the derivative with respect to }x

\text{Find the derivative with respect to }y

Graph

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