Solve y 3=- 1/3 (x-(-5))

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 5

Evaluate

y \times 3 = - \frac{1}{3} (x - (- 5))

To find the x -intercept,set y =0

0 \times 3 = - \frac{1}{3} (x - (- 5))

Any expression multiplied by 0 equals 0

0 = - \frac{1}{3} (x - (- 5))

Simplify

More Steps

Evaluate

- \frac{1}{3} (x - (- 5))

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

- \frac{1}{3} (x + 5)

Multiply the terms

More Steps

Evaluate

\frac{1}{3} (x + 5)

Apply the distributive property

\frac{1}{3} x + \frac{1}{3} \times 5

Multiply the numbers

\frac{1}{3} x + \frac{5}{3}

- (\frac{1}{3} x + \frac{5}{3})

Calculate

- \frac{1}{3} x - \frac{5}{3}

0 = - \frac{1}{3} x - \frac{5}{3}

Swap the sides of the equation

- \frac{1}{3} x - \frac{5}{3} = 0

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

- \frac{1}{3} x = 0 + \frac{5}{3}

Add the terms

- \frac{1}{3} x = \frac{5}{3}

Change the signs on both sides of the equation

\frac{1}{3} x = - \frac{5}{3}

Multiply by the reciprocal

\frac{1}{3} x \times 3 = - \frac{5}{3} \times 3

Multiply

x = - \frac{5}{3} \times 3

Solution

More Steps

Evaluate

- \frac{5}{3} \times 3

Reduce the numbers

- 5 \times 1

Simplify

- 5

x = - 5

Show Solution

Solve the equation

Solve for x

Solve for y

x = - 9 y - 5

Evaluate

y \times 3 = - \frac{1}{3} (x - (- 5))

Use the commutative property to reorder the terms

3 y = - \frac{1}{3} (x - (- 5))

Simplify

More Steps

Evaluate

- \frac{1}{3} (x - (- 5))

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

- \frac{1}{3} (x + 5)

Multiply the terms

More Steps

Evaluate

\frac{1}{3} (x + 5)

Apply the distributive property

\frac{1}{3} x + \frac{1}{3} \times 5

Multiply the numbers

\frac{1}{3} x + \frac{5}{3}

- (\frac{1}{3} x + \frac{5}{3})

Calculate

- \frac{1}{3} x - \frac{5}{3}

3 y = - \frac{1}{3} x - \frac{5}{3}

Swap the sides of the equation

- \frac{1}{3} x - \frac{5}{3} = 3 y

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

- \frac{1}{3} x = 3 y + \frac{5}{3}

Change the signs on both sides of the equation

\frac{1}{3} x = - 3 y - \frac{5}{3}

Multiply by the reciprocal

\frac{1}{3} x \times 3 = (- 3 y - \frac{5}{3}) \times 3

Multiply

x = (- 3 y - \frac{5}{3}) \times 3

Solution

More Steps

Evaluate

(- 3 y - \frac{5}{3}) \times 3

Apply the distributive property

- 3 y \times 3 - \frac{5}{3} \times 3

Multiply the terms

- 9 y - \frac{5}{3} \times 3

Multiply the numbers

More Steps

Evaluate

- \frac{5}{3} \times 3

Reduce the numbers

- 5 \times 1

Simplify

- 5

- 9 y - 5

x = - 9 y - 5

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

y 3 = - \frac{1}{3} (x - (- 5))

Simplify the expression

3 y = - \frac{1}{3} x - \frac{5}{3}

To test if the graph of 3 y = - \frac{1}{3} x - \frac{5}{3} is symmetry with respect to the origin,substitute -x for x and -y for y

3 (- y) = - \frac{1}{3} (- x) - \frac{5}{3}

Evaluate

- 3 y = - \frac{1}{3} (- x) - \frac{5}{3}

Multiplying or dividing an even number of negative terms equals a positive

- 3 y = \frac{1}{3} x - \frac{5}{3}

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{5}{9 sin ( θ ) + cos ( θ )}

Evaluate

y \times 3 = - \frac{1}{3} (x - (- 5))

Use the commutative property to reorder the terms

3 y = - \frac{1}{3} (x - (- 5))

Evaluate

More Steps

Evaluate

- \frac{1}{3} (x - (- 5))

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

- \frac{1}{3} (x + 5)

Multiply the terms

More Steps

Evaluate

\frac{1}{3} (x + 5)

Apply the distributive property

\frac{1}{3} x + \frac{1}{3} \times 5

Multiply the numbers

\frac{1}{3} x + \frac{5}{3}

- (\frac{1}{3} x + \frac{5}{3})

Calculate

- \frac{1}{3} x - \frac{5}{3}

3 y = - \frac{1}{3} x - \frac{5}{3}

Multiply both sides of the equation by LCD

3 y \times 3 = (- \frac{1}{3} x - \frac{5}{3}) \times 3

Simplify the equation

9 y = (- \frac{1}{3} x - \frac{5}{3}) \times 3

Simplify the equation

More Steps

Evaluate

(- \frac{1}{3} x - \frac{5}{3}) \times 3

Apply the distributive property

- \frac{1}{3} x \times 3 - \frac{5}{3} \times 3

Simplify

- x - 5

9 y = - x - 5

Move the expression to the left side

9 y + x = - 5

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

9 sin (θ) \times r + cos (θ) \times r = - 5

Factor the expression

(9 sin (θ) + cos (θ)) r = - 5

Solution

r = - \frac{5}{9 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} = - \frac{1}{9}

Calculate

y 3 = - \frac{1}{3} (x - (- 5))

Simplify the expression

3 y = - \frac{1}{3} x - \frac{5}{3}

Take the derivative of both sides

\frac{d}{d x} (3 y) = \frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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 y}{d x}

3 \frac{d y}{d x} = \frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Use differentiation rules

\frac{d}{d x} (- \frac{1}{3} x) + \frac{d}{d x} (- \frac{5}{3})

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- \frac{1}{3} x)

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

- \frac{1}{3} \times \frac{d}{d x} (x)

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

- \frac{1}{3} \times 1

Any expression multiplied by 1 remains the same

- \frac{1}{3}

- \frac{1}{3} + \frac{d}{d x} (- \frac{5}{3})

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

- \frac{1}{3} + 0

Evaluate

- \frac{1}{3}

3 \frac{d y}{d x} = - \frac{1}{3}

Multiply by the reciprocal

3 \frac{d y}{d x} \times \frac{1}{3} = - \frac{1}{3} \times \frac{1}{3}

Multiply

\frac{d y}{d x} = - \frac{1}{3} \times \frac{1}{3}

Solution

More Steps

Evaluate

- \frac{1}{3} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{1}{3 \times 3}

Multiply the numbers

- \frac{1}{9}

\frac{d y}{d x} = - \frac{1}{9}

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

y 3 = - \frac{1}{3} (x - (- 5))

Simplify the expression

3 y = - \frac{1}{3} x - \frac{5}{3}

Take the derivative of both sides

\frac{d}{d x} (3 y) = \frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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 y}{d x}

3 \frac{d y}{d x} = \frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- \frac{1}{3} x - \frac{5}{3})

Use differentiation rules

\frac{d}{d x} (- \frac{1}{3} x) + \frac{d}{d x} (- \frac{5}{3})

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- \frac{1}{3} x)

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

- \frac{1}{3} \times \frac{d}{d x} (x)

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

- \frac{1}{3} \times 1

Any expression multiplied by 1 remains the same

- \frac{1}{3}

- \frac{1}{3} + \frac{d}{d x} (- \frac{5}{3})

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

- \frac{1}{3} + 0

Evaluate

- \frac{1}{3}

3 \frac{d y}{d x} = - \frac{1}{3}

Multiply by the reciprocal

3 \frac{d y}{d x} \times \frac{1}{3} = - \frac{1}{3} \times \frac{1}{3}

Multiply

\frac{d y}{d x} = - \frac{1}{3} \times \frac{1}{3}

Multiply

More Steps

Evaluate

- \frac{1}{3} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{1}{3 \times 3}

Multiply the numbers

- \frac{1}{9}

\frac{d y}{d x} = - \frac{1}{9}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{1}{9})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{1}{9})

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