Testing for symmetry about the origin of 2x+3y=12

\textrm{Not symmetry with respect to the origin}

Testing for symmetry about the x-axis of 2x+3y=12

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

Testing for symmetry about the y-axis of 2x+3y=12

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

Rewrite in polar form of 2x+3y=12

r=\frac{12}{2\cos\left(\theta \right)+3\sin\left(\theta \right)}

Question :

2x+3y=12

2 x + 3 y = 12

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 6

Evaluate

2 x + 3 y = 12

To find the x -intercept,set y =0

2 x + 3 \times 0 = 12

Any expression multiplied by 0 equals 0

2 x + 0 = 12

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

2 x = 12

Divide both sides

\frac{2 x}{2} = \frac{12}{2}

Divide the numbers

x = \frac{12}{2}

Solution

More Steps

Evaluate

\frac{12}{2}

Reduce the numbers

\frac{6}{1}

Calculate

6

x = 6

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{12 - 3 y}{2}

Evaluate

2 x + 3 y = 12

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

2 x = 12 - 3 y

Divide both sides

\frac{2 x}{2} = \frac{12 - 3 y}{2}

Solution

x = \frac{12 - 3 y}{2}

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 x + 3 y = 12

To test if the graph of 2 x + 3 y = 12 is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- x) + 3 (- y) = 12

Evaluate

More Steps

Evaluate

2 (- x) + 3 (- y)

Multiply the numbers

- 2 x + 3 (- y)

Multiply the numbers

- 2 x - 3 y

- 2 x - 3 y = 12

Solution

Not symmetry with respect to the origin

Show Solution

Rewrite the equation

Rewrite in polar form

Rewrite in slope-intercept form

r = \frac{12}{2 cos ( θ ) + 3 sin ( θ )}

Evaluate

2 x + 3 y = 12

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

2 cos (θ) \times r + 3 sin (θ) \times r = 12

Factor the expression

(2 cos (θ) + 3 sin (θ)) r = 12

Solution

r = \frac{12}{2 cos ( θ ) + 3 sin ( 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{2}{3}

Calculate

2 x + 3 y = 12

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (12)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 x + 3 y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (3 y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

2 \times 1

Any expression multiplied by 1 remains the same

2

2 + \frac{d}{d x} (3 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 y)

Use differentiation rules

\frac{d}{d y} (3 y) \times \frac{d y}{d x}

Evaluate the derivative

3 \frac{d y}{d x}

2 + 3 \frac{d y}{d x}

2 + 3 \frac{d y}{d x} = \frac{d}{d x} (12)

Calculate the derivative

2 + 3 \frac{d y}{d x} = 0

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

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

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

3 \frac{d y}{d x} = - 2

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{- 2}{3}

Divide the numbers

\frac{d y}{d x} = \frac{- 2}{3}

Solution

\frac{d y}{d x} = - \frac{2}{3}

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 x + 3 y = 12

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (12)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 x + 3 y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (3 y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

2 \times 1

Any expression multiplied by 1 remains the same

2

2 + \frac{d}{d x} (3 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 y)

Use differentiation rules

\frac{d}{d y} (3 y) \times \frac{d y}{d x}

Evaluate the derivative

3 \frac{d y}{d x}

2 + 3 \frac{d y}{d x}

2 + 3 \frac{d y}{d x} = \frac{d}{d x} (12)

Calculate the derivative

2 + 3 \frac{d y}{d x} = 0

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

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

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

3 \frac{d y}{d x} = - 2

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{- 2}{3}

Divide the numbers

\frac{d y}{d x} = \frac{- 2}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

\frac{d y}{d x} = - \frac{2}{3}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{2}{3})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{2}{3})

Solution

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

Show Solution

2x+3y=12

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 $2x+3y=12$

Find the y-intercept of $2x+3y=12$

Find the slope of $2x+3y=12$

$Solve for x$ of $2x+3y=12$

$Solve for y$ of $2x+3y=12$

Testing for symmetry about the origin of $2x+3y=12$

Testing for symmetry about the x-axis of $2x+3y=12$

Testing for symmetry about the y-axis of $2x+3y=12$

Rewrite in polar form of $2x+3y=12$

Rewrite in slope-intercept form of $2x+3y=12$

$Find the derivative with respect to x$ of $2x+3y=12$

$Find the derivative with respect to y$ of $2x+3y=12$

$Find the second derivative with respect to x$ of $2x+3y=12$

$Find the second derivative with respect to y$ of $2x+3y=12$

2x+3y=12

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 2x+3y=122x+3y=122x+3y=12

Find the y-intercept of 2x+3y=122x+3y=122x+3y=12

Find the slope of 2x+3y=122x+3y=122x+3y=12

Solve for x of 2x+3y=122x+3y=122x+3y=12

Solve for y of 2x+3y=122x+3y=122x+3y=12

Testing for symmetry about the origin of 2x+3y=122x+3y=122x+3y=12

Testing for symmetry about the x-axis of 2x+3y=122x+3y=122x+3y=12

Testing for symmetry about the y-axis of 2x+3y=122x+3y=122x+3y=12

Rewrite in polar form of 2x+3y=122x+3y=122x+3y=12

Rewrite in slope-intercept form of 2x+3y=122x+3y=122x+3y=12

Find the derivative with respect to x of 2x+3y=122x+3y=122x+3y=12

Find the derivative with respect to y of 2x+3y=122x+3y=122x+3y=12

Find the second derivative with respect to x of 2x+3y=122x+3y=122x+3y=12

Find the second derivative with respect to y of 2x+3y=122x+3y=122x+3y=12

$Find the x -intercept/zero$ of $2x+3y=12$

Find the y-intercept of $2x+3y=12$

Find the slope of $2x+3y=12$

$Solve for x$ of $2x+3y=12$

$Solve for y$ of $2x+3y=12$

Testing for symmetry about the origin of $2x+3y=12$

Testing for symmetry about the x-axis of $2x+3y=12$

Testing for symmetry about the y-axis of $2x+3y=12$

Rewrite in polar form of $2x+3y=12$

Rewrite in slope-intercept form of $2x+3y=12$

$Find the derivative with respect to x$ of $2x+3y=12$

$Find the derivative with respect to y$ of $2x+3y=12$

$Find the second derivative with respect to x$ of $2x+3y=12$

$Find the second derivative with respect to y$ of $2x+3y=12$