Solve 5x- 8y- 40 = 0

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 8

Evaluate

5 x - 8 y - 40 = 0

To find the x -intercept,set y =0

5 x - 8 \times 0 - 40 = 0

Any expression multiplied by 0 equals 0

5 x - 0 - 40 = 0

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

5 x - 40 = 0

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

5 x = 0 + 40

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

5 x = 40

Divide both sides

\frac{5 x}{5} = \frac{40}{5}

Divide the numbers

x = \frac{40}{5}

Solution

More Steps

Evaluate

\frac{40}{5}

Reduce the numbers

\frac{8}{1}

Calculate

8

x = 8

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{8 y + 40}{5}

Evaluate

5 x - 8 y - 40 = 0

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

5 x = 0 + 8 y + 40

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

5 x = 8 y + 40

Divide both sides

\frac{5 x}{5} = \frac{8 y + 40}{5}

Solution

x = \frac{8 y + 40}{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

5 x - 8 y - 40 = 0

To test if the graph of 5 x - 8 y - 40 = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

5 (- x) - 8 (- y) - 40 = 0

Evaluate

More Steps

Evaluate

5 (- x) - 8 (- y) - 40

Multiply the numbers

- 5 x - 8 (- y) - 40

Multiply the numbers

- 5 x + 8 y - 40

- 5 x + 8 y - 40 = 0

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{40}{5 cos ( θ ) - 8 sin ( θ )}

Evaluate

5 x - 8 y - 40 = 0

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

5 cos (θ) \times r - 8 sin (θ) \times r - 40 = 0

Factor the expression

(5 cos (θ) - 8 sin (θ)) r - 40 = 0

Subtract the terms

(5 cos (θ) - 8 sin (θ)) r - 40 - (- 40) = 0 - (- 40)

Evaluate

(5 cos (θ) - 8 sin (θ)) r = 40

Solution

r = \frac{40}{5 cos ( θ ) - 8 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{5}{8}

Calculate

5 x - 8 y - 40 = 0

Take the derivative of both sides

\frac{d}{d x} (5 x - 8 y - 40) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - 8 y - 40)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- 8 y) + \frac{d}{d x} (- 40)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x)

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

5 \times \frac{d}{d x} (x)

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- 8 y) + \frac{d}{d x} (- 40)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 8 y)

Use differentiation rules

\frac{d}{d y} (- 8 y) \times \frac{d y}{d x}

Evaluate the derivative

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

5 - 8 \frac{d y}{d x} + \frac{d}{d x} (- 40)

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

5 - 8 \frac{d y}{d x} + 0

Evaluate

5 - 8 \frac{d y}{d x}

5 - 8 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

5 - 8 \frac{d y}{d x} = 0

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

- 8 \frac{d y}{d x} = 0 - 5

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

- 8 \frac{d y}{d x} = - 5

Change the signs on both sides of the equation

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

Divide both sides

\frac{8 \frac{d y}{d x}}{8} = \frac{5}{8}

Solution

\frac{d y}{d x} = \frac{5}{8}

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

5 x - 8 y - 40 = 0

Take the derivative of both sides

\frac{d}{d x} (5 x - 8 y - 40) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - 8 y - 40)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- 8 y) + \frac{d}{d x} (- 40)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x)

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

5 \times \frac{d}{d x} (x)

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- 8 y) + \frac{d}{d x} (- 40)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 8 y)

Use differentiation rules

\frac{d}{d y} (- 8 y) \times \frac{d y}{d x}

Evaluate the derivative

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

5 - 8 \frac{d y}{d x} + \frac{d}{d x} (- 40)

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

5 - 8 \frac{d y}{d x} + 0

Evaluate

5 - 8 \frac{d y}{d x}

5 - 8 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

5 - 8 \frac{d y}{d x} = 0

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

- 8 \frac{d y}{d x} = 0 - 5

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

- 8 \frac{d y}{d x} = - 5

Change the signs on both sides of the equation

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

Divide both sides

\frac{8 \frac{d y}{d x}}{8} = \frac{5}{8}

Divide the numbers

\frac{d y}{d x} = \frac{5}{8}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{5}{8})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{5}{8})

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