Solve 8x - 1/2y = -38

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{19}{4}

Evaluate

8 x - \frac{1}{2} y = - 38

To find the x -intercept,set y =0

8 x - \frac{1}{2} \times 0 = - 38

Any expression multiplied by 0 equals 0

8 x - 0 = - 38

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

8 x = - 38

Divide both sides

\frac{8 x}{8} = \frac{- 38}{8}

Divide the numbers

x = \frac{- 38}{8}

Solution

More Steps

Evaluate

\frac{- 38}{8}

Cancel out the common factor 2

\frac{- 19}{4}

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

- \frac{19}{4}

x = - \frac{19}{4}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{- 76 + y}{16}

Evaluate

8 x - \frac{1}{2} y = - 38

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

8 x = - 38 + \frac{1}{2} y

Divide both sides

\frac{8 x}{8} = \frac{- 38 + \frac{1}{2} y}{8}

Divide the numbers

x = \frac{- 38 + \frac{1}{2} y}{8}

Solution

More Steps

Evaluate

\frac{- 38 + \frac{1}{2} y}{8}

Rewrite the expression

\frac{\frac{- 76 + y}{2}}{8}

Multiply by the reciprocal

\frac{- 76 + y}{2} \times \frac{1}{8}

Rewrite the expression

- \frac{76 - y}{2} \times \frac{1}{8}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{76 - y}{2 \times 8}

Multiply the numbers

- \frac{76 - y}{16}

Calculate the product

\frac{- 76 + y}{16}

x = \frac{- 76 + y}{16}

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

8 x - \frac{1}{2} y = - 38

To test if the graph of 8 x - \frac{1}{2} y = - 38 is symmetry with respect to the origin,substitute -x for x and -y for y

8 (- x) - \frac{1}{2} (- y) = - 38

Evaluate

More Steps

Evaluate

8 (- x) - \frac{1}{2} (- y)

Multiply the numbers

- 8 x - \frac{1}{2} (- y)

Multiplying or dividing an odd number of negative terms equals a negative

- 8 x - (- \frac{1}{2} y)

Rewrite the expression

- 8 x + \frac{1}{2} y

- 8 x + \frac{1}{2} y = - 38

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{76}{16 cos ( θ ) - sin ( θ )}

Evaluate

8 x - \frac{1}{2} y = - 38

Multiply both sides of the equation by LCD

(8 x - \frac{1}{2} y) \times 2 = - 38 \times 2

Simplify the equation

More Steps

Evaluate

(8 x - \frac{1}{2} y) \times 2

Apply the distributive property

8 x \times 2 - \frac{1}{2} y \times 2

Simplify

8 x \times 2 - y

Multiply the numbers

16 x - y

16 x - y = - 38 \times 2

Simplify the equation

16 x - y = - 76

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

16 cos (θ) \times r - sin (θ) \times r = - 76

Factor the expression

(16 cos (θ) - sin (θ)) r = - 76

Solution

r = - \frac{76}{16 cos ( θ ) - 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} = 16

Calculate

8 x - \frac{1}{2} y = - 38

Take the derivative of both sides

\frac{d}{d x} (8 x - \frac{1}{2} y) = \frac{d}{d x} (- 38)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (8 x - \frac{1}{2} y)

Use differentiation rules

\frac{d}{d x} (8 x) + \frac{d}{d x} (- \frac{1}{2} y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

8 \times 1

Any expression multiplied by 1 remains the same

8

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{1}{2} \frac{d y}{d x}

8 - \frac{1}{2} \frac{d y}{d x}

8 - \frac{1}{2} \frac{d y}{d x} = \frac{d}{d x} (- 38)

Calculate the derivative

8 - \frac{1}{2} \frac{d y}{d x} = 0

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

- \frac{1}{2} \frac{d y}{d x} = 0 - 8

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

- \frac{1}{2} \frac{d y}{d x} = - 8

Change the signs on both sides of the equation

\frac{1}{2} \frac{d y}{d x} = 8

Multiply by the reciprocal

\frac{1}{2} \frac{d y}{d x} \times 2 = 8 \times 2

Multiply

\frac{d y}{d x} = 8 \times 2

Solution

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

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

8 x - \frac{1}{2} y = - 38

Take the derivative of both sides

\frac{d}{d x} (8 x - \frac{1}{2} y) = \frac{d}{d x} (- 38)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (8 x - \frac{1}{2} y)

Use differentiation rules

\frac{d}{d x} (8 x) + \frac{d}{d x} (- \frac{1}{2} y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

8 \times 1

Any expression multiplied by 1 remains the same

8

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{1}{2} \frac{d y}{d x}

8 - \frac{1}{2} \frac{d y}{d x}

8 - \frac{1}{2} \frac{d y}{d x} = \frac{d}{d x} (- 38)

Calculate the derivative

8 - \frac{1}{2} \frac{d y}{d x} = 0

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

- \frac{1}{2} \frac{d y}{d x} = 0 - 8

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

- \frac{1}{2} \frac{d y}{d x} = - 8

Change the signs on both sides of the equation

\frac{1}{2} \frac{d y}{d x} = 8

Multiply by the reciprocal

\frac{1}{2} \frac{d y}{d x} \times 2 = 8 \times 2

Multiply

\frac{d y}{d x} = 8 \times 2

Multiply

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

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (16)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (16)

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