Solve -12x - 4y = 20

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{5}{3}

Evaluate

- 12 x - 4 y = 20

To find the x -intercept,set y =0

- 12 x - 4 \times 0 = 20

Any expression multiplied by 0 equals 0

- 12 x - 0 = 20

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

- 12 x = 20

Change the signs on both sides of the equation

12 x = - 20

Divide both sides

\frac{12 x}{12} = \frac{- 20}{12}

Divide the numbers

x = \frac{- 20}{12}

Solution

More Steps

Evaluate

\frac{- 20}{12}

Cancel out the common factor 4

\frac{- 5}{3}

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

- \frac{5}{3}

x = - \frac{5}{3}

Show Solution

Solve the equation

Solve for x

Solve for y

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

Evaluate

- 12 x - 4 y = 20

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

- 12 x = 20 + 4 y

Change the signs on both sides of the equation

12 x = - 20 - 4 y

Divide both sides

\frac{12 x}{12} = \frac{- 20 - 4 y}{12}

Divide the numbers

x = \frac{- 20 - 4 y}{12}

Solution

More Steps

Evaluate

\frac{- 20 - 4 y}{12}

Rewrite the expression

\frac{4 ( - 5 - y )}{12}

Cancel out the common factor 4

\frac{- 5 - y}{3}

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

- \frac{5 + y}{3}

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

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

- 12 x - 4 y = 20

To test if the graph of - 12 x - 4 y = 20 is symmetry with respect to the origin,substitute -x for x and -y for y

- 12 (- x) - 4 (- y) = 20

Evaluate

More Steps

Evaluate

- 12 (- x) - 4 (- y)

Multiply the numbers

12 x - 4 (- y)

Multiply the numbers

12 x - (- 4 y)

Rewrite the expression

12 x + 4 y

12 x + 4 y = 20

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}{3 cos ( θ ) + sin ( θ )}

Evaluate

- 12 x - 4 y = 20

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

- 12 cos (θ) \times r - 4 sin (θ) \times r = 20

Factor the expression

(- 12 cos (θ) - 4 sin (θ)) r = 20

Solution

r = - \frac{5}{3 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} = - 3

Calculate

- 12 x - 4 y = 20

Take the derivative of both sides

\frac{d}{d x} (- 12 x - 4 y) = \frac{d}{d x} (20)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 12 x - 4 y)

Use differentiation rules

\frac{d}{d x} (- 12 x) + \frac{d}{d x} (- 4 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 12 x)

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

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

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

- 12 \times 1

Any expression multiplied by 1 remains the same

- 12

- 12 + \frac{d}{d x} (- 4 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 y)

Use differentiation rules

\frac{d}{d y} (- 4 y) \times \frac{d y}{d x}

Evaluate the derivative

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

- 12 - 4 \frac{d y}{d x}

- 12 - 4 \frac{d y}{d x} = \frac{d}{d x} (20)

Calculate the derivative

- 12 - 4 \frac{d y}{d x} = 0

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

- 4 \frac{d y}{d x} = 0 + 12

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

- 4 \frac{d y}{d x} = 12

Change the signs on both sides of the equation

4 \frac{d y}{d x} = - 12

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{- 12}{4}

Divide the numbers

\frac{d y}{d x} = \frac{- 12}{4}

Solution

More Steps

Evaluate

\frac{- 12}{4}

Reduce the numbers

\frac{- 3}{1}

Calculate

- 3

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

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

- 12 x - 4 y = 20

Take the derivative of both sides

\frac{d}{d x} (- 12 x - 4 y) = \frac{d}{d x} (20)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 12 x - 4 y)

Use differentiation rules

\frac{d}{d x} (- 12 x) + \frac{d}{d x} (- 4 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 12 x)

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

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

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

- 12 \times 1

Any expression multiplied by 1 remains the same

- 12

- 12 + \frac{d}{d x} (- 4 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 y)

Use differentiation rules

\frac{d}{d y} (- 4 y) \times \frac{d y}{d x}

Evaluate the derivative

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

- 12 - 4 \frac{d y}{d x}

- 12 - 4 \frac{d y}{d x} = \frac{d}{d x} (20)

Calculate the derivative

- 12 - 4 \frac{d y}{d x} = 0

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

- 4 \frac{d y}{d x} = 0 + 12

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

- 4 \frac{d y}{d x} = 12

Change the signs on both sides of the equation

4 \frac{d y}{d x} = - 12

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{- 12}{4}

Divide the numbers

\frac{d y}{d x} = \frac{- 12}{4}

Divide the numbers

More Steps

Evaluate

\frac{- 12}{4}

Reduce the numbers

\frac{- 3}{1}

Calculate

- 3

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

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 3)

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

Show Solution

12x 4y = 20

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph