Solve 4y-16x=20 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{5}{4}

Evaluate

4 y - 16 x = 20

To find the x -intercept,set y =0

4 \times 0 - 16 x = 20

Any expression multiplied by 0 equals 0

0 - 16 x = 20

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

- 16 x = 20

Change the signs on both sides of the equation

16 x = - 20

Divide both sides

\frac{16 x}{16} = \frac{- 20}{16}

Divide the numbers

x = \frac{- 20}{16}

Solution

More Steps

Evaluate

\frac{- 20}{16}

Cancel out the common factor 4

\frac{- 5}{4}

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

- \frac{5}{4}

x = - \frac{5}{4}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{- 5 + y}{4}

Evaluate

4 y - 16 x = 20

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

- 16 x = 20 - 4 y

Change the signs on both sides of the equation

16 x = - 20 + 4 y

Divide both sides

\frac{16 x}{16} = \frac{- 20 + 4 y}{16}

Divide the numbers

x = \frac{- 20 + 4 y}{16}

Solution

More Steps

Evaluate

\frac{- 20 + 4 y}{16}

Rewrite the expression

\frac{4 ( - 5 + y )}{16}

Cancel out the common factor 4

\frac{- 5 + y}{4}

x = \frac{- 5 + y}{4}

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

4 y - 16 x = 20

To test if the graph of 4 y - 16 x = 20 is symmetry with respect to the origin,substitute -x for x and -y for y

4 (- y) - 16 (- x) = 20

Evaluate

More Steps

Evaluate

4 (- y) - 16 (- x)

Multiply the numbers

- 4 y - 16 (- x)

Multiply the numbers

- 4 y - (- 16 x)

Rewrite the expression

- 4 y + 16 x

- 4 y + 16 x = 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}{sin ( θ ) - 4 cos ( θ )}

Evaluate

4 y - 16 x = 20

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

4 sin (θ) \times r - 16 cos (θ) \times r = 20

Factor the expression

(4 sin (θ) - 16 cos (θ)) r = 20

Solution

r = \frac{5}{sin ( θ ) - 4 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} = 4

Calculate

4 y - 16 x = 20

Take the derivative of both sides

\frac{d}{d x} (4 y - 16 x) = \frac{d}{d x} (20)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (4 y - 16 x)

Use differentiation rules

\frac{d}{d x} (4 y) + \frac{d}{d x} (- 16 x)

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}

4 \frac{d y}{d x} + \frac{d}{d x} (- 16 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 16 x)

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

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

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

- 16 \times 1

Any expression multiplied by 1 remains the same

- 16

4 \frac{d y}{d x} - 16

4 \frac{d y}{d x} - 16 = \frac{d}{d x} (20)

Calculate the derivative

4 \frac{d y}{d x} - 16 = 0

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

4 \frac{d y}{d x} = 0 + 16

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

4 \frac{d y}{d x} = 16

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{16}{4}

Divide the numbers

\frac{d y}{d x} = \frac{16}{4}

Solution

More Steps

Evaluate

\frac{16}{4}

Reduce the numbers

\frac{4}{1}

Calculate

4

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

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

4 y - 16 x = 20

Take the derivative of both sides

\frac{d}{d x} (4 y - 16 x) = \frac{d}{d x} (20)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (4 y - 16 x)

Use differentiation rules

\frac{d}{d x} (4 y) + \frac{d}{d x} (- 16 x)

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}

4 \frac{d y}{d x} + \frac{d}{d x} (- 16 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 16 x)

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

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

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

- 16 \times 1

Any expression multiplied by 1 remains the same

- 16

4 \frac{d y}{d x} - 16

4 \frac{d y}{d x} - 16 = \frac{d}{d x} (20)

Calculate the derivative

4 \frac{d y}{d x} - 16 = 0

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

4 \frac{d y}{d x} = 0 + 16

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

4 \frac{d y}{d x} = 16

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{16}{4}

Divide the numbers

\frac{d y}{d x} = \frac{16}{4}

Divide the numbers

More Steps

Evaluate

\frac{16}{4}

Reduce the numbers

\frac{4}{1}

Calculate

4

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

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (4)

Solution

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

Show Solution

4y 16x=20

Function

Solve the equation

Testing for symmetry

Rewrite the equation

Find the first derivative

Find the second derivative

Graph