Solve -6x-2y=-4 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{2}{3}

Evaluate

- 6 x - 2 y = - 4

To find the x -intercept,set y =0

- 6 x - 2 \times 0 = - 4

Any expression multiplied by 0 equals 0

- 6 x - 0 = - 4

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

- 6 x = - 4

Change the signs on both sides of the equation

6 x = 4

Divide both sides

\frac{6 x}{6} = \frac{4}{6}

Divide the numbers

x = \frac{4}{6}

Solution

x = \frac{2}{3}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{2 - y}{3}

Evaluate

- 6 x - 2 y = - 4

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

- 6 x = - 4 + 2 y

Change the signs on both sides of the equation

6 x = 4 - 2 y

Divide both sides

\frac{6 x}{6} = \frac{4 - 2 y}{6}

Divide the numbers

x = \frac{4 - 2 y}{6}

Solution

More Steps

Evaluate

\frac{4 - 2 y}{6}

Rewrite the expression

\frac{2 ( 2 - y )}{6}

Cancel out the common factor 2

\frac{2 - y}{3}

x = \frac{2 - y}{3}

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

- 6 x - 2 y = - 4

To test if the graph of - 6 x - 2 y = - 4 is symmetry with respect to the origin,substitute -x for x and -y for y

- 6 (- x) - 2 (- y) = - 4

Evaluate

More Steps

Evaluate

- 6 (- x) - 2 (- y)

Multiply the numbers

6 x - 2 (- y)

Multiply the numbers

6 x - (- 2 y)

Rewrite the expression

6 x + 2 y

6 x + 2 y = - 4

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{2}{3 cos ( θ ) + sin ( θ )}

Evaluate

- 6 x - 2 y = - 4

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

- 6 cos (θ) \times r - 2 sin (θ) \times r = - 4

Factor the expression

(- 6 cos (θ) - 2 sin (θ)) r = - 4

Solution

r = \frac{2}{3 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} = - 3

Calculate

- 6 x - 2 y = - 4

Take the derivative of both sides

\frac{d}{d x} (- 6 x - 2 y) = \frac{d}{d x} (- 4)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 x - 2 y)

Use differentiation rules

\frac{d}{d x} (- 6 x) + \frac{d}{d x} (- 2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 x)

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

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

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

- 6 \times 1

Any expression multiplied by 1 remains the same

- 6

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

- 6 - 2 \frac{d y}{d x}

- 6 - 2 \frac{d y}{d x} = \frac{d}{d x} (- 4)

Calculate the derivative

- 6 - 2 \frac{d y}{d x} = 0

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

- 2 \frac{d y}{d x} = 0 + 6

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

- 2 \frac{d y}{d x} = 6

Change the signs on both sides of the equation

2 \frac{d y}{d x} = - 6

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 6}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 6}{2}

Solution

More Steps

Evaluate

\frac{- 6}{2}

Reduce the numbers

\frac{- 3}{1}

Calculate

- 3

\frac{d y}{d x} = - 3

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

- 6 x - 2 y = - 4

Take the derivative of both sides

\frac{d}{d x} (- 6 x - 2 y) = \frac{d}{d x} (- 4)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 x - 2 y)

Use differentiation rules

\frac{d}{d x} (- 6 x) + \frac{d}{d x} (- 2 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 6 x)

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

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

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

- 6 \times 1

Any expression multiplied by 1 remains the same

- 6

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

- 6 - 2 \frac{d y}{d x}

- 6 - 2 \frac{d y}{d x} = \frac{d}{d x} (- 4)

Calculate the derivative

- 6 - 2 \frac{d y}{d x} = 0

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

- 2 \frac{d y}{d x} = 0 + 6

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

- 2 \frac{d y}{d x} = 6

Change the signs on both sides of the equation

2 \frac{d y}{d x} = - 6

Divide both sides

\frac{2 \frac{d y}{d x}}{2} = \frac{- 6}{2}

Divide the numbers

\frac{d y}{d x} = \frac{- 6}{2}

Divide the numbers

More Steps

Evaluate

\frac{- 6}{2}

Reduce the numbers

\frac{- 3}{1}

Calculate

- 3

\frac{d y}{d x} = - 3

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- 3)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 3)

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