Solve 5(x-9)-6(y-2)=0

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{33}{5}

Evaluate

5 (x - 9) - 6 (y - 2) = 0

To find the x -intercept,set y =0

5 (x - 9) - 6 (0 - 2) = 0

Simplify

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Evaluate

5 (x - 9) - 6 (0 - 2)

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

5 (x - 9) - 6 (- 2)

Multiply the numbers

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Evaluate

6 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 6 \times 2

Multiply the numbers

- 12

5 (x - 9) - (- 12)

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

5 (x - 9) + 12

5 (x - 9) + 12 = 0

Calculate

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Evaluate

5 (x - 9) + 12

Expand the expression

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Calculate

5 (x - 9)

Apply the distributive property

5 x - 5 \times 9

Multiply the numbers

5 x - 45

5 x - 45 + 12

Add the numbers

5 x - 33

5 x - 33 = 0

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

5 x = 0 + 33

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

5 x = 33

Divide both sides

\frac{5 x}{5} = \frac{33}{5}

Solution

x = \frac{33}{5}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{33 + 6 y}{5}

Evaluate

5 (x - 9) - 6 (y - 2) = 0

Rewrite the expression

5 (x - 9) - 6 y + 12 = 0

Calculate the sum or difference

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Evaluate

5 (x - 9) - 6 y + 12

Expand the expression

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Calculate

5 (x - 9)

Apply the distributive property

5 x - 5 \times 9

Multiply the numbers

5 x - 45

5 x - 45 - 6 y + 12

Add the numbers

5 x - 33 - 6 y

5 x - 33 - 6 y = 0

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

5 x = 0 + 33 + 6 y

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

5 x = 33 + 6 y

Divide both sides

\frac{5 x}{5} = \frac{33 + 6 y}{5}

Solution

x = \frac{33 + 6 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

5 (x - 9) - 6 (y - 2) = 0

To test if the graph of 5 (x - 9) - 6 (y - 2) = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

5 (- x - 9) - 6 (- y - 2) = 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{33}{5 cos ( θ ) - 6 sin ( θ )}

Evaluate

5 (x - 9) - 6 (y - 2) = 0

Evaluate

More Steps

Evaluate

5 (x - 9) - 6 (y - 2)

Expand the expression

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Calculate

5 (x - 9)

Apply the distributive property

5 x - 5 \times 9

Multiply the numbers

5 x - 45

5 x - 45 - 6 (y - 2)

Expand the expression

More Steps

Calculate

- 6 (y - 2)

Apply the distributive property

- 6 y - (- 6 \times 2)

Multiply the numbers

- 6 y - (- 12)

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

- 6 y + 12

5 x - 45 - 6 y + 12

Add the numbers

5 x - 33 - 6 y

5 x - 33 - 6 y = 0

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

5 cos (θ) \times r - 33 - 6 sin (θ) \times r = 0

Factor the expression

(5 cos (θ) - 6 sin (θ)) r - 33 = 0

Subtract the terms

(5 cos (θ) - 6 sin (θ)) r - 33 - (- 33) = 0 - (- 33)

Evaluate

(5 cos (θ) - 6 sin (θ)) r = 33

Solution

r = \frac{33}{5 cos ( θ ) - 6 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{5}{6}

Calculate

5 (x - 9) - 6 (y - 2) = 0

Simplify the expression

5 x - 33 - 6 y = 0

Take the derivative of both sides

\frac{d}{d x} (5 x - 33 - 6 y) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - 33 - 6 y)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- 33) + \frac{d}{d x} (- 6 y)

Evaluate the derivative

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Evaluate

\frac{d}{d x} (5 x)

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

5 \times \frac{d}{d x} (x)

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- 33) + \frac{d}{d x} (- 6 y)

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

5 + 0 + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 y)

Use differentiation rules

\frac{d}{d y} (- 6 y) \times \frac{d y}{d x}

Evaluate the derivative

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

5 + 0 - 6 \frac{d y}{d x}

Evaluate

5 - 6 \frac{d y}{d x}

5 - 6 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

5 - 6 \frac{d y}{d x} = 0

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

- 6 \frac{d y}{d x} = 0 - 5

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

- 6 \frac{d y}{d x} = - 5

Change the signs on both sides of the equation

6 \frac{d y}{d x} = 5

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{5}{6}

Solution

\frac{d y}{d x} = \frac{5}{6}

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

5 (x - 9) - 6 (y - 2) = 0

Simplify the expression

5 x - 33 - 6 y = 0

Take the derivative of both sides

\frac{d}{d x} (5 x - 33 - 6 y) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - 33 - 6 y)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- 33) + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x)

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

5 \times \frac{d}{d x} (x)

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- 33) + \frac{d}{d x} (- 6 y)

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

5 + 0 + \frac{d}{d x} (- 6 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 y)

Use differentiation rules

\frac{d}{d y} (- 6 y) \times \frac{d y}{d x}

Evaluate the derivative

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

5 + 0 - 6 \frac{d y}{d x}

Evaluate

5 - 6 \frac{d y}{d x}

5 - 6 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

5 - 6 \frac{d y}{d x} = 0

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

- 6 \frac{d y}{d x} = 0 - 5

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

- 6 \frac{d y}{d x} = - 5

Change the signs on both sides of the equation

6 \frac{d y}{d x} = 5

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{5}{6}

Divide the numbers

\frac{d y}{d x} = \frac{5}{6}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{5}{6})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{5}{6})

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