Solve 0=-x-y-2 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 2

Evaluate

0 = - x - y - 2

To find the x -intercept,set y =0

0 = - x - 0 - 2

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

0 = - x - 2

Swap the sides of the equation

- x - 2 = 0

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

- x = 0 + 2

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

- x = 2

Solution

x = - 2

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Solve the equation

Solve for x

Solve for y

x = - y - 2

Evaluate

0 = - x - y - 2

Swap the sides of the equation

- x - y - 2 = 0

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

- x = 0 + y + 2

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

- x = y + 2

Solution

x = - 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

0 = - x - y - 2

To test if the graph of 0 = - x - y - 2 is symmetry with respect to the origin,substitute -x for x and -y for y

0 = - (- x) - (- y) - 2

Evaluate

More Steps

Evaluate

- (- x) - (- y) - 2

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x - (- y) - 2

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

x + y - 2

0 = x + y - 2

Solution

Not symmetry with respect to the origin

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Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = - \frac{2}{cos ( θ ) + sin ( θ )}

Evaluate

0 = - x - y - 2

Move the expression to the left side

x + y = - 2

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

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

Factor the expression

(cos (θ) + sin (θ)) r = - 2

Solution

r = - \frac{2}{cos ( θ ) + sin ( θ )}

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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

0 = - x - y - 2

Take the derivative of both sides

\frac{d}{d x} (0) = \frac{d}{d x} (- x - y - 2)

Calculate the derivative

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

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

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{d y}{d x}

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

Use \frac{d}{d x} (c) = 0 to find derivative

- 1 - \frac{d y}{d x} + 0

Evaluate

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

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

Swap the sides of the equation

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

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

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

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

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

Solution

\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

0 = - x - y - 2

Take the derivative of both sides

\frac{d}{d x} (0) = \frac{d}{d x} (- x - y - 2)

Calculate the derivative

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

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

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{d y}{d x}

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

Use \frac{d}{d x} (c) = 0 to find derivative

- 1 - \frac{d y}{d x} + 0

Evaluate

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

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

Swap the sides of the equation

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

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

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

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

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

Change the signs on both sides of the equation

\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