Solve (x-2) - 4(y 7) = 117

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 119

Evaluate

(x - 2) - 4 (y \times 7) = 117

To find the x -intercept,set y =0

(x - 2) - 4 (0 \times 7) = 117

Any expression multiplied by 0 equals 0

(x - 2) - 4 \times 0 = 117

Any expression multiplied by 0 equals 0

(x - 2) - 0 = 117

Simplify

More Steps

Evaluate

(x - 2) - 0

Remove the parentheses

x - 2 - 0

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

x - 2

x - 2 = 117

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

x = 117 + 2

Solution

x = 119

Show Solution

Solve the equation

Solve for x

Solve for y

x = 119 + 28 y

Evaluate

(x - 2) - 4 (y \times 7) = 117

Remove the parentheses

(x - 2) - 4 y \times 7 = 117

Simplify

More Steps

Evaluate

(x - 2) - 4 y \times 7

Remove the parentheses

x - 2 - 4 y \times 7

Multiply the terms

x - 2 - 28 y

x - 2 - 28 y = 117

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

x = 117 + 2 + 28 y

Solution

x = 119 + 28 y

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

(x - 2) - 4 (y 7) = 117

Simplify the expression

x - 2 - 28 y = 117

To test if the graph of x - 2 - 28 y = 117 is symmetry with respect to the origin,substitute -x for x and -y for y

- x - 2 - 28 (- y) = 117

Evaluate

- x - 2 + 28 y = 117

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{119}{cos ( θ ) - 28 sin ( θ )}

Evaluate

(x - 2) - 4 (y \times 7) = 117

Evaluate

More Steps

Evaluate

(x - 2) - 4 (y \times 7)

Remove the parentheses

(x - 2) - 4 y \times 7

Remove the parentheses

x - 2 - 4 y \times 7

Multiply the terms

x - 2 - 28 y

x - 2 - 28 y = 117

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

cos (θ) \times r - 2 - 28 sin (θ) \times r = 117

Factor the expression

(cos (θ) - 28 sin (θ)) r - 2 = 117

Subtract the terms

(cos (θ) - 28 sin (θ)) r - 2 - (- 2) = 117 - (- 2)

Evaluate

(cos (θ) - 28 sin (θ)) r = 119

Solution

r = \frac{119}{cos ( θ ) - 28 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{1}{28}

Calculate

(x - 2) - 4 (y 7) = 117

Simplify the expression

x - 2 - 28 y = 117

Take the derivative of both sides

\frac{d}{d x} (x - 2 - 28 y) = \frac{d}{d x} (117)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (x - 2 - 28 y)

Use differentiation rules

\frac{d}{d x} (x) + \frac{d}{d x} (- 2) + \frac{d}{d x} (- 28 y)

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

1 + \frac{d}{d x} (- 2) + \frac{d}{d x} (- 28 y)

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

1 + 0 + \frac{d}{d x} (- 28 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 28 y)

Use differentiation rules

\frac{d}{d y} (- 28 y) \times \frac{d y}{d x}

Evaluate the derivative

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

1 + 0 - 28 \frac{d y}{d x}

Evaluate

1 - 28 \frac{d y}{d x}

1 - 28 \frac{d y}{d x} = \frac{d}{d x} (117)

Calculate the derivative

1 - 28 \frac{d y}{d x} = 0

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

- 28 \frac{d y}{d x} = 0 - 1

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

- 28 \frac{d y}{d x} = - 1

Change the signs on both sides of the equation

28 \frac{d y}{d x} = 1

Divide both sides

\frac{28 \frac{d y}{d x}}{28} = \frac{1}{28}

Solution

\frac{d y}{d x} = \frac{1}{28}

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

(x - 2) - 4 (y 7) = 117

Simplify the expression

x - 2 - 28 y = 117

Take the derivative of both sides

\frac{d}{d x} (x - 2 - 28 y) = \frac{d}{d x} (117)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (x - 2 - 28 y)

Use differentiation rules

\frac{d}{d x} (x) + \frac{d}{d x} (- 2) + \frac{d}{d x} (- 28 y)

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

1 + \frac{d}{d x} (- 2) + \frac{d}{d x} (- 28 y)

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

1 + 0 + \frac{d}{d x} (- 28 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 28 y)

Use differentiation rules

\frac{d}{d y} (- 28 y) \times \frac{d y}{d x}

Evaluate the derivative

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

1 + 0 - 28 \frac{d y}{d x}

Evaluate

1 - 28 \frac{d y}{d x}

1 - 28 \frac{d y}{d x} = \frac{d}{d x} (117)

Calculate the derivative

1 - 28 \frac{d y}{d x} = 0

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

- 28 \frac{d y}{d x} = 0 - 1

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

- 28 \frac{d y}{d x} = - 1

Change the signs on both sides of the equation

28 \frac{d y}{d x} = 1

Divide both sides

\frac{28 \frac{d y}{d x}}{28} = \frac{1}{28}

Divide the numbers

\frac{d y}{d x} = \frac{1}{28}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{1}{28})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{1}{28})

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