Solve 9x-9y=-9 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 1

Evaluate

9 x - 9 y = - 9

To find the x -intercept,set y =0

9 x - 9 \times 0 = - 9

Any expression multiplied by 0 equals 0

9 x - 0 = - 9

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

9 x = - 9

Divide both sides

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

Divide the numbers

x = \frac{- 9}{9}

Solution

More Steps

Evaluate

\frac{- 9}{9}

Reduce the numbers

\frac{- 1}{1}

Calculate

- 1

x = - 1

Show Solution

Solve the equation

Solve for x

Solve for y

x = - 1 + y

Evaluate

9 x - 9 y = - 9

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

9 x = - 9 + 9 y

Divide both sides

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

Divide the numbers

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

Solution

More Steps

Evaluate

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

Rewrite the expression

\frac{9 ( - 1 + y )}{9}

Reduce the fraction

- 1 + y

x = - 1 + 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 x - 9 y = - 9

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

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

Evaluate

More Steps

Evaluate

9 (- x) - 9 (- y)

Multiply the numbers

- 9 x - 9 (- y)

Multiply the numbers

- 9 x - (- 9 y)

Rewrite the expression

- 9 x + 9 y

- 9 x + 9 y = - 9

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{1}{cos ( θ ) - sin ( θ )}

Evaluate

9 x - 9 y = - 9

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

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

Factor the expression

(9 cos (θ) - 9 sin (θ)) r = - 9

Solution

r = - \frac{1}{cos ( θ ) - 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} = 1

Calculate

9 x - 9 y = - 9

Take the derivative of both sides

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

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}{d x} (- 9 y)

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

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

Calculate the derivative

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

Change the signs on both sides of the equation

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 x - 9 y = - 9

Take the derivative of both sides

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

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}{d x} (- 9 y)

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

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

Calculate the derivative

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

Change the signs on both sides of the equation

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