Solve 3x-6y=-12 - ScanMath

Question

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

x = - 4

Evaluate

3 x - 6 y = - 12

To find the x -intercept,set y =0

3 x - 6 \times 0 = - 12

Any expression multiplied by 0 equals 0

3 x - 0 = - 12

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

3 x = - 12

Divide both sides

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

Divide the numbers

x = \frac{- 12}{3}

Solution

More Steps

Evaluate

\frac{- 12}{3}

Reduce the numbers

\frac{- 4}{1}

Calculate

- 4

x = - 4

Show Solution

Solve the equation

$Solve for x$

$Solve for y$

x = - 4 + 2 y

Evaluate

3 x - 6 y = - 12

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

3 x = - 12 + 6 y

Divide both sides

\frac{3 x}{3} = \frac{- 12 + 6 y}{3}

Divide the numbers

x = \frac{- 12 + 6 y}{3}

Solution

More Steps

Evaluate

\frac{- 12 + 6 y}{3}

Rewrite the expression

\frac{3 ( - 4 + 2 y )}{3}

Reduce the fraction

- 4 + 2 y

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

3 x - 6 y = - 12

To test if the graph of 3 x - 6 y = - 12 is symmetry with respect to the origin,substitute -x for x and -y for y

3 (- x) - 6 (- y) = - 12

Evaluate

More Steps

Evaluate

3 (- x) - 6 (- y)

Multiply the numbers

- 3 x - 6 (- y)

Multiply the numbers

- 3 x - (- 6 y)

Rewrite the expression

- 3 x + 6 y

- 3 x + 6 y = - 12

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}{cos ( θ ) - 2 sin ( θ )}

Evaluate

3 x - 6 y = - 12

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

3 cos (θ) \times r - 6 sin (θ) \times r = - 12

Factor the expression

(3 cos (θ) - 6 sin (θ)) r = - 12

Solution

r = - \frac{4}{cos ( θ ) - 2 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{1}{2}

Calculate

3 x - 6 y = - 12

Take the derivative of both sides

\frac{d}{d x} (3 x - 6 y) = \frac{d}{d x} (- 12)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x - 6 y)

Use differentiation rules

\frac{d}{d x} (3 x) + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

3 \times 1

Any expression multiplied by 1 remains the same

3

3 + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 y)

Use differentiation rules

\frac{d}{d y} (- 6 y) \times \frac{d y}{d x}

Evaluate the derivative

- 6 \frac{d y}{d x}

3 - 6 \frac{d y}{d x}

3 - 6 \frac{d y}{d x} = \frac{d}{d x} (- 12)

Calculate the derivative

3 - 6 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

6 \frac{d y}{d x} = 3

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{3}{6}

Divide the numbers

\frac{d y}{d x} = \frac{3}{6}

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

3 x - 6 y = - 12

Take the derivative of both sides

\frac{d}{d x} (3 x - 6 y) = \frac{d}{d x} (- 12)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x - 6 y)

Use differentiation rules

\frac{d}{d x} (3 x) + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

3 \times 1

Any expression multiplied by 1 remains the same

3

3 + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 y)

Use differentiation rules

\frac{d}{d y} (- 6 y) \times \frac{d y}{d x}

Evaluate the derivative

- 6 \frac{d y}{d x}

3 - 6 \frac{d y}{d x}

3 - 6 \frac{d y}{d x} = \frac{d}{d x} (- 12)

Calculate the derivative

3 - 6 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

6 \frac{d y}{d x} = 3

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{3}{6}

Divide the numbers

\frac{d y}{d x} = \frac{3}{6}

Cancel out the common factor 3

\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

3x 6y= 12

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

Solve the equation

$Solve for x$

$Solve for y$

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

$Find the derivative with respect to x$

$Find the derivative with respect to y$

Find the second derivative

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$

Graph

3x 6y= 12

Function

Find the x-intercept/zero

Find the y-intercept

Find the slope

Solve the equation

Solve for x

Solve for y

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

Graph

$Find the x -intercept/zero$

$Solve for x$

$Solve for y$

$Find the derivative with respect to x$

$Find the derivative with respect to y$

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$