Solve 9y-9x=27 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 3

Evaluate

9 y - 9 x = 27

To find the x -intercept,set y =0

9 \times 0 - 9 x = 27

Any expression multiplied by 0 equals 0

0 - 9 x = 27

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

- 9 x = 27

Change the signs on both sides of the equation

9 x = - 27

Divide both sides

\frac{9 x}{9} = \frac{- 27}{9}

Divide the numbers

x = \frac{- 27}{9}

Solution

More Steps

Evaluate

\frac{- 27}{9}

Reduce the numbers

\frac{- 3}{1}

Calculate

- 3

x = - 3

Show Solution

Solve the equation

Solve for x

Solve for y

x = - 3 + y

Evaluate

9 y - 9 x = 27

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

- 9 x = 27 - 9 y

Change the signs on both sides of the equation

9 x = - 27 + 9 y

Divide both sides

\frac{9 x}{9} = \frac{- 27 + 9 y}{9}

Divide the numbers

x = \frac{- 27 + 9 y}{9}

Solution

More Steps

Evaluate

\frac{- 27 + 9 y}{9}

Rewrite the expression

\frac{9 ( - 3 + y )}{9}

Reduce the fraction

- 3 + y

x = - 3 + 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

9 y - 9 x = 27

To test if the graph of 9 y - 9 x = 27 is symmetry with respect to the origin,substitute -x for x and -y for y

9 (- y) - 9 (- x) = 27

Evaluate

More Steps

Evaluate

9 (- y) - 9 (- x)

Multiply the numbers

- 9 y - 9 (- x)

Multiply the numbers

- 9 y - (- 9 x)

Rewrite the expression

- 9 y + 9 x

- 9 y + 9 x = 27

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{3}{sin ( θ ) - cos ( θ )}

Evaluate

9 y - 9 x = 27

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

9 sin (θ) \times r - 9 cos (θ) \times r = 27

Factor the expression

(9 sin (θ) - 9 cos (θ)) r = 27

Solution

r = \frac{3}{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} = 1

Calculate

9 y - 9 x = 27

Take the derivative of both sides

\frac{d}{d x} (9 y - 9 x) = \frac{d}{d x} (27)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y - 9 x)

Use differentiation rules

\frac{d}{d x} (9 y) + \frac{d}{d x} (- 9 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y)

Use differentiation rules

\frac{d}{d y} (9 y) \times \frac{d y}{d x}

Evaluate the derivative

9 \frac{d y}{d x}

9 \frac{d y}{d x} + \frac{d}{d x} (- 9 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 9 x)

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

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

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

- 9 \times 1

Any expression multiplied by 1 remains the same

- 9

9 \frac{d y}{d x} - 9

9 \frac{d y}{d x} - 9 = \frac{d}{d x} (27)

Calculate the derivative

9 \frac{d y}{d x} - 9 = 0

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

9 \frac{d y}{d x} = 0 + 9

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

9 \frac{d y}{d x} = 9

Divide both sides

\frac{9 \frac{d y}{d x}}{9} = \frac{9}{9}

Divide the numbers

\frac{d y}{d x} = \frac{9}{9}

Solution

More Steps

Evaluate

\frac{9}{9}

Reduce the numbers

\frac{1}{1}

Calculate

1

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

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

9 y - 9 x = 27

Take the derivative of both sides

\frac{d}{d x} (9 y - 9 x) = \frac{d}{d x} (27)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y - 9 x)

Use differentiation rules

\frac{d}{d x} (9 y) + \frac{d}{d x} (- 9 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y)

Use differentiation rules

\frac{d}{d y} (9 y) \times \frac{d y}{d x}

Evaluate the derivative

9 \frac{d y}{d x}

9 \frac{d y}{d x} + \frac{d}{d x} (- 9 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 9 x)

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

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

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

- 9 \times 1

Any expression multiplied by 1 remains the same

- 9

9 \frac{d y}{d x} - 9

9 \frac{d y}{d x} - 9 = \frac{d}{d x} (27)

Calculate the derivative

9 \frac{d y}{d x} - 9 = 0

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

9 \frac{d y}{d x} = 0 + 9

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

9 \frac{d y}{d x} = 9

Divide both sides

\frac{9 \frac{d y}{d x}}{9} = \frac{9}{9}

Divide the numbers

\frac{d y}{d x} = \frac{9}{9}

Divide the numbers

More Steps

Evaluate

\frac{9}{9}

Reduce the numbers

\frac{1}{1}

Calculate

1

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

Take the derivative of both sides

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

Calculate the derivative

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

Solution

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

Show Solution

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph