Solve 6*2 - x - 2 y + 13 = 0

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 25

Evaluate

6 \times 2 - x - 2 y + 13 = 0

To find the x -intercept,set y =0

6 \times 2 - x - 2 \times 0 + 13 = 0

Any expression multiplied by 0 equals 0

6 \times 2 - x - 0 + 13 = 0

Simplify

More Steps

Evaluate

6 \times 2 - x - 0 + 13

Multiply the numbers

12 - x - 0 + 13

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

12 - x + 13

Add the numbers

25 - x

25 - x = 0

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

- x = 0 - 25

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

- x = - 25

Solution

x = 25

Show Solution

Solve the equation

Solve for x

Solve for y

x = 25 - 2 y

Evaluate

6 \times 2 - x - 2 y + 13 = 0

Simplify

More Steps

Evaluate

6 \times 2 - x - 2 y + 13

Multiply the numbers

12 - x - 2 y + 13

Add the numbers

25 - x - 2 y

25 - x - 2 y = 0

Rewrite the expression

25 - 2 y - x = 0

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

- x = 0 - (25 - 2 y)

Subtract the terms

More Steps

Evaluate

0 - (25 - 2 y)

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

0 - 25 + 2 y

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

- 25 + 2 y

- x = - 25 + 2 y

Solution

x = 25 - 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

6 \cdot 2 - x - 2 y + 13 = 0

Simplify the expression

25 - x - 2 y = 0

To test if the graph of 25 - x - 2 y = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

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

Evaluate

More Steps

Evaluate

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

Multiply the numbers

25 - (- x) + 2 y

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

25 + x + 2 y

25 + x + 2 y = 0

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{25}{cos ( θ ) + 2 sin ( θ )}

Evaluate

6 \times 2 - x - 2 y + 13 = 0

Evaluate

More Steps

Evaluate

6 \times 2 - x - 2 y + 13

Multiply the numbers

12 - x - 2 y + 13

Add the numbers

25 - x - 2 y

25 - x - 2 y = 0

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

25 - cos (θ) \times r - 2 sin (θ) \times r = 0

Factor the expression

(- cos (θ) - 2 sin (θ)) r + 25 = 0

Subtract the terms

(- cos (θ) - 2 sin (θ)) r + 25 - 25 = 0 - 25

Evaluate

(- cos (θ) - 2 sin (θ)) r = - 25

Solution

r = \frac{25}{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

6 \cdot 2 - x - 2 y + 13 = 0

Simplify the expression

25 - x - 2 y = 0

Take the derivative of both sides

\frac{d}{d x} (25 - x - 2 y) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (25 - x - 2 y)

Use differentiation rules

\frac{d}{d x} (25) + \frac{d}{d x} (- x) + \frac{d}{d x} (- 2 y)

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

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

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

0 - 1 + \frac{d}{d x} (- 2 y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

0 - 1 - 2 \frac{d y}{d x}

Evaluate

- 1 - 2 \frac{d y}{d x}

- 1 - 2 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

- 1 - 2 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 1}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 1}{2}

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

6 \cdot 2 - x - 2 y + 13 = 0

Simplify the expression

25 - x - 2 y = 0

Take the derivative of both sides

\frac{d}{d x} (25 - x - 2 y) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (25 - x - 2 y)

Use differentiation rules

\frac{d}{d x} (25) + \frac{d}{d x} (- x) + \frac{d}{d x} (- 2 y)

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

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

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

0 - 1 + \frac{d}{d x} (- 2 y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

0 - 1 - 2 \frac{d y}{d x}

Evaluate

- 1 - 2 \frac{d y}{d x}

- 1 - 2 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

- 1 - 2 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 1}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 1}{2}

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

\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

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph