Solve 12x-20y=-100

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{25}{3}

Evaluate

12 x - 20 y = - 100

To find the x -intercept,set y =0

12 x - 20 \times 0 = - 100

Any expression multiplied by 0 equals 0

12 x - 0 = - 100

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

12 x = - 100

Divide both sides

\frac{12 x}{12} = \frac{- 100}{12}

Divide the numbers

x = \frac{- 100}{12}

Solution

More Steps

Evaluate

\frac{- 100}{12}

Cancel out the common factor 4

\frac{- 25}{3}

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

- \frac{25}{3}

x = - \frac{25}{3}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{- 25 + 5 y}{3}

Evaluate

12 x - 20 y = - 100

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

12 x = - 100 + 20 y

Divide both sides

\frac{12 x}{12} = \frac{- 100 + 20 y}{12}

Divide the numbers

x = \frac{- 100 + 20 y}{12}

Solution

More Steps

Evaluate

\frac{- 100 + 20 y}{12}

Rewrite the expression

\frac{4 ( - 25 + 5 y )}{12}

Cancel out the common factor 4

\frac{- 25 + 5 y}{3}

x = \frac{- 25 + 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 - 20 y = - 100

To test if the graph of 12 x - 20 y = - 100 is symmetry with respect to the origin,substitute -x for x and -y for y

12 (- x) - 20 (- y) = - 100

Evaluate

More Steps

Evaluate

12 (- x) - 20 (- y)

Multiply the numbers

- 12 x - 20 (- y)

Multiply the numbers

- 12 x - (- 20 y)

Rewrite the expression

- 12 x + 20 y

- 12 x + 20 y = - 100

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}{3 cos ( θ ) - 5 sin ( θ )}

Evaluate

12 x - 20 y = - 100

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

12 cos (θ) \times r - 20 sin (θ) \times r = - 100

Factor the expression

(12 cos (θ) - 20 sin (θ)) r = - 100

Solution

r = - \frac{25}{3 cos ( θ ) - 5 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{3}{5}

Calculate

12 x - 20 y = - 100

Take the derivative of both sides

\frac{d}{d x} (12 x - 20 y) = \frac{d}{d x} (- 100)

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 20 y)

Use differentiation rules

\frac{d}{d y} (- 20 y) \times \frac{d y}{d x}

Evaluate the derivative

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

12 - 20 \frac{d y}{d x}

12 - 20 \frac{d y}{d x} = \frac{d}{d x} (- 100)

Calculate the derivative

12 - 20 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

20 \frac{d y}{d x} = 12

Divide both sides

\frac{20 \frac{d y}{d x}}{20} = \frac{12}{20}

Divide the numbers

\frac{d y}{d x} = \frac{12}{20}

Solution

\frac{d y}{d x} = \frac{3}{5}

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 - 20 y = - 100

Take the derivative of both sides

\frac{d}{d x} (12 x - 20 y) = \frac{d}{d x} (- 100)

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 20 y)

Use differentiation rules

\frac{d}{d y} (- 20 y) \times \frac{d y}{d x}

Evaluate the derivative

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

12 - 20 \frac{d y}{d x}

12 - 20 \frac{d y}{d x} = \frac{d}{d x} (- 100)

Calculate the derivative

12 - 20 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

20 \frac{d y}{d x} = 12

Divide both sides

\frac{20 \frac{d y}{d x}}{20} = \frac{12}{20}

Divide the numbers

\frac{d y}{d x} = \frac{12}{20}

Cancel out the common factor 4

\frac{d y}{d x} = \frac{3}{5}

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{3}{5})

Solution

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

Show Solution

12x 20y= 100

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph