Solve 12y-10x=90 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - 9

Evaluate

12 y - 10 x = 90

To find the x -intercept,set y =0

12 \times 0 - 10 x = 90

Any expression multiplied by 0 equals 0

0 - 10 x = 90

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

- 10 x = 90

Change the signs on both sides of the equation

10 x = - 90

Divide both sides

\frac{10 x}{10} = \frac{- 90}{10}

Divide the numbers

x = \frac{- 90}{10}

Solution

More Steps

Evaluate

\frac{- 90}{10}

Reduce the numbers

\frac{- 9}{1}

Calculate

- 9

x = - 9

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{- 45 + 6 y}{5}

Evaluate

12 y - 10 x = 90

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

- 10 x = 90 - 12 y

Change the signs on both sides of the equation

10 x = - 90 + 12 y

Divide both sides

\frac{10 x}{10} = \frac{- 90 + 12 y}{10}

Divide the numbers

x = \frac{- 90 + 12 y}{10}

Solution

More Steps

Evaluate

\frac{- 90 + 12 y}{10}

Rewrite the expression

\frac{2 ( - 45 + 6 y )}{10}

Cancel out the common factor 2

\frac{- 45 + 6 y}{5}

x = \frac{- 45 + 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

12 y - 10 x = 90

To test if the graph of 12 y - 10 x = 90 is symmetry with respect to the origin,substitute -x for x and -y for y

12 (- y) - 10 (- x) = 90

Evaluate

More Steps

Evaluate

12 (- y) - 10 (- x)

Multiply the numbers

- 12 y - 10 (- x)

Multiply the numbers

- 12 y - (- 10 x)

Rewrite the expression

- 12 y + 10 x

- 12 y + 10 x = 90

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{45}{6 sin ( θ ) - 5 cos ( θ )}

Evaluate

12 y - 10 x = 90

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

12 sin (θ) \times r - 10 cos (θ) \times r = 90

Factor the expression

(12 sin (θ) - 10 cos (θ)) r = 90

Solution

r = \frac{45}{6 sin ( θ ) - 5 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{5}{6}

Calculate

12 y - 10 x = 90

Take the derivative of both sides

\frac{d}{d x} (12 y - 10 x) = \frac{d}{d x} (90)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (12 y - 10 x)

Use differentiation rules

\frac{d}{d x} (12 y) + \frac{d}{d x} (- 10 x)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

12 \frac{d y}{d x}

12 \frac{d y}{d x} + \frac{d}{d x} (- 10 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 10 x)

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

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

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

- 10 \times 1

Any expression multiplied by 1 remains the same

- 10

12 \frac{d y}{d x} - 10

12 \frac{d y}{d x} - 10 = \frac{d}{d x} (90)

Calculate the derivative

12 \frac{d y}{d x} - 10 = 0

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

12 \frac{d y}{d x} = 0 + 10

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

12 \frac{d y}{d x} = 10

Divide both sides

\frac{12 \frac{d y}{d x}}{12} = \frac{10}{12}

Divide the numbers

\frac{d y}{d x} = \frac{10}{12}

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

12 y - 10 x = 90

Take the derivative of both sides

\frac{d}{d x} (12 y - 10 x) = \frac{d}{d x} (90)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (12 y - 10 x)

Use differentiation rules

\frac{d}{d x} (12 y) + \frac{d}{d x} (- 10 x)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

12 \frac{d y}{d x}

12 \frac{d y}{d x} + \frac{d}{d x} (- 10 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 10 x)

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

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

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

- 10 \times 1

Any expression multiplied by 1 remains the same

- 10

12 \frac{d y}{d x} - 10

12 \frac{d y}{d x} - 10 = \frac{d}{d x} (90)

Calculate the derivative

12 \frac{d y}{d x} - 10 = 0

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

12 \frac{d y}{d x} = 0 + 10

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

12 \frac{d y}{d x} = 10

Divide both sides

\frac{12 \frac{d y}{d x}}{12} = \frac{10}{12}

Divide the numbers

\frac{d y}{d x} = \frac{10}{12}

Cancel out the common factor 2

\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