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2x-y=7

Algebra Calculus Trigonometry Matrix

Question

2x-y=7

Function

x=\frac{7}{2}

Evaluate

2x-y=7

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

2x-0=7

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

2x=7

Divide both sides

\frac{2x}{2}=\frac{7}{2}

Solution

x=\frac{7}{2}

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

Find the y-intercept

Find the slope

Solve the equation

x=\frac{7+y}{2}

Evaluate

2x-y=7

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

2x=7+y

Divide both sides

\frac{2x}{2}=\frac{7+y}{2}

Solution

x=\frac{7+y}{2}

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\text{Solve for }x

\text{Solve for }y

Testing for symmetry

\textrm{Not symmetry with respect to the origin}

Evaluate

2x-y=7

\text{To test if the graph of }2x-y=7\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}

2\left(-x\right)-\left(-y\right)=7

Evaluate

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Evaluate

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

Multiply the numbers

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

Rewrite the expression

-2x+y

-2x+y=7

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{7}{2\cos\left(\theta \right)-\sin\left(\theta \right)}

Evaluate

2x-y=7

\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)

2\cos\left(\theta \right)\times r-\sin\left(\theta \right)\times r=7

Factor the expression

\left(2\cos\left(\theta \right)-\sin\left(\theta \right)\right)r=7

Solution

r=\frac{7}{2\cos\left(\theta \right)-\sin\left(\theta \right)}

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Rewrite in polar form

Rewrite in slope-intercept form

Find the first derivative

\frac{dy}{dx}=2

Calculate

2x-y=7

Take the derivative of both sides

\frac{d}{dx}\left(2x-y\right)=\frac{d}{dx}\left(7\right)

Calculate the derivative

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Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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Evaluate

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

\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))

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

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

2\times 1

Any expression multiplied by 1 remains the same

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

Evaluate the derivative

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Evaluate

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

Use differentiation rules

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

Evaluate the derivative

-\frac{dy}{dx}

2-\frac{dy}{dx}

2-\frac{dy}{dx}=\frac{d}{dx}\left(7\right)

Calculate the derivative

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

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

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

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

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

Solution

\frac{dy}{dx}=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

2x-y=7

Take the derivative of both sides

\frac{d}{dx}\left(2x-y\right)=\frac{d}{dx}\left(7\right)

Calculate the derivative

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Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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Evaluate

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

\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))

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

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

2\times 1

Any expression multiplied by 1 remains the same

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

Evaluate the derivative

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Evaluate

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

Use differentiation rules

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

Evaluate the derivative

-\frac{dy}{dx}

2-\frac{dy}{dx}

2-\frac{dy}{dx}=\frac{d}{dx}\left(7\right)

Calculate the derivative

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

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

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

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

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

Change the signs on both sides of the equation

\frac{dy}{dx}=2

Take the derivative of both sides

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

Calculate the derivative

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

Solution

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

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\text{Find the second derivative with respect to }x

\text{Find the second derivative with respect to }y

Graph

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