Testing for symmetry about the origin of 2y-x=4

\textrm{Not symmetry with respect to the origin}

Testing for symmetry about the x-axis of 2y-x=4

\textrm{Not symmetry with respect to the x-axis}

Testing for symmetry about the y-axis of 2y-x=4

\textrm{Not symmetry with respect to the y-axis}

Rewrite in polar form of 2y-x=4

r=\frac{4}{2\sin\left(\theta \right)-\cos\left(\theta \right)}

Question :

2y-x=4

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 4

Evaluate

2 y - x = 4

To find the x -intercept,set y =0

2 \times 0 - x = 4

Any expression multiplied by 0 equals 0

0 - x = 4

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

- x = 4

Solution

x = - 4

Show Solution

Solve the equation

Solve for x

Solve for y

x = - 4 + 2 y

Evaluate

2 y - x = 4

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

- x = 4 - 2 y

Solution

x = - 4 + 2 y

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Evaluate

2 y - x = 4

To test if the graph of 2 y - x = 4 is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- y) - (- x) = 4

Evaluate

More Steps

Evaluate

2 (- y) - (- x)

Multiply the numbers

- 2 y - (- x)

Rewrite the expression

- 2 y + x

- 2 y + x = 4

Solution

Not symmetry with respect to the origin

Show Solution

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = \frac{4}{2 sin ( θ ) - cos ( θ )}

Evaluate

2 y - x = 4

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

2 sin (θ) \times r - cos (θ) \times r = 4

Factor the expression

(2 sin (θ) - cos (θ)) r = 4

Solution

r = \frac{4}{2 sin ( θ ) - cos ( θ )}

Show Solution

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

\frac{d y}{d x} = \frac{1}{2}

Calculate

2 y - x = 4

Take the derivative of both sides

\frac{d}{d x} (2 y - x) = \frac{d}{d x} (4)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y - x)

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y)

Use differentiation rules

\frac{d}{d y} (2 y) \times \frac{d y}{d x}

Evaluate the derivative

2 \frac{d y}{d x}

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

- \frac{d}{d x} (x)

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

- 1

2 \frac{d y}{d x} - 1

2 \frac{d y}{d x} - 1 = \frac{d}{d x} (4)

Calculate the derivative

2 \frac{d y}{d x} - 1 = 0

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

2 \frac{d y}{d x} = 0 + 1

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

2 \frac{d y}{d x} = 1

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{1}{2}

Solution

\frac{d y}{d x} = \frac{1}{2}

Show Solution

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

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

Calculate

2 y - x = 4

Take the derivative of both sides

\frac{d}{d x} (2 y - x) = \frac{d}{d x} (4)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y - x)

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 y)

Use differentiation rules

\frac{d}{d y} (2 y) \times \frac{d y}{d x}

Evaluate the derivative

2 \frac{d y}{d x}

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

- \frac{d}{d x} (x)

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

- 1

2 \frac{d y}{d x} - 1

2 \frac{d y}{d x} - 1 = \frac{d}{d x} (4)

Calculate the derivative

2 \frac{d y}{d x} - 1 = 0

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

2 \frac{d y}{d x} = 0 + 1

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

2 \frac{d y}{d x} = 1

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{1}{2}

Divide the numbers

\frac{d y}{d x} = \frac{1}{2}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{1}{2})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{1}{2})

Solution

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

Show Solution

2y-x=4

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph

Frequently Asked Questions

$Find the x -intercept/zero$ of \(2y-x=4\)

Find the y-intercept of \(2y-x=4\)

Find the slope of \(2y-x=4\)

$Solve for x$ of \(2y-x=4\)

$Solve for y$ of \(2y-x=4\)

Testing for symmetry about the origin of \(2y-x=4\)

Testing for symmetry about the x-axis of \(2y-x=4\)

Testing for symmetry about the y-axis of \(2y-x=4\)

Rewrite in polar form of \(2y-x=4\)

Rewrite in standard form of \(2y-x=4\)

Rewrite in slope-intercept form of \(2y-x=4\)

$Find the derivative with respect to x$ of \(2y-x=4\)

$Find the derivative with respect to y$ of \(2y-x=4\)

$Find the second derivative with respect to x$ of \(2y-x=4\)

$Find the second derivative with respect to y$ of \(2y-x=4\)

2y-x=4

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph

Frequently Asked Questions

Find the x-intercept/zero of \(2y-x=4\)

Find the y-intercept of \(2y-x=4\)

Find the slope of \(2y-x=4\)

Solve for x of \(2y-x=4\)

Solve for y of \(2y-x=4\)

Testing for symmetry about the origin of \(2y-x=4\)

Testing for symmetry about the x-axis of \(2y-x=4\)

Testing for symmetry about the y-axis of \(2y-x=4\)

Rewrite in polar form of \(2y-x=4\)

Rewrite in standard form of \(2y-x=4\)

Rewrite in slope-intercept form of \(2y-x=4\)

Find the derivative with respect to x of \(2y-x=4\)

Find the derivative with respect to y of \(2y-x=4\)

Find the second derivative with respect to x of \(2y-x=4\)

Find the second derivative with respect to y of \(2y-x=4\)

$Find the x -intercept/zero$ of \(2y-x=4\)

$Solve for x$ of \(2y-x=4\)

$Solve for y$ of \(2y-x=4\)

$Find the derivative with respect to x$ of \(2y-x=4\)

$Find the derivative with respect to y$ of \(2y-x=4\)

$Find the second derivative with respect to x$ of \(2y-x=4\)

$Find the second derivative with respect to y$ of \(2y-x=4\)