Solve 12=4x-6y - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 3

Evaluate

12 = 4 x - 6 y

To find the x -intercept,set y =0

12 = 4 x - 6 \times 0

Any expression multiplied by 0 equals 0

12 = 4 x - 0

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

12 = 4 x

Swap the sides of the equation

4 x = 12

Divide both sides

\frac{4 x}{4} = \frac{12}{4}

Divide the numbers

x = \frac{12}{4}

Solution

More Steps

Evaluate

\frac{12}{4}

Reduce the numbers

\frac{3}{1}

Calculate

3

x = 3

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{6 + 3 y}{2}

Evaluate

12 = 4 x - 6 y

Swap the sides of the equation

4 x - 6 y = 12

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

4 x = 12 + 6 y

Divide both sides

\frac{4 x}{4} = \frac{12 + 6 y}{4}

Divide the numbers

x = \frac{12 + 6 y}{4}

Solution

More Steps

Evaluate

\frac{12 + 6 y}{4}

Rewrite the expression

\frac{2 ( 6 + 3 y )}{4}

Cancel out the common factor 2

\frac{6 + 3 y}{2}

x = \frac{6 + 3 y}{2}

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

12 = 4 x - 6 y

To test if the graph of 12 = 4 x - 6 y is symmetry with respect to the origin,substitute -x for x and -y for y

12 = 4 (- x) - 6 (- y)

Evaluate

More Steps

Evaluate

4 (- x) - 6 (- y)

Multiply the numbers

- 4 x - 6 (- y)

Multiply the numbers

- 4 x - (- 6 y)

Rewrite the expression

- 4 x + 6 y

12 = - 4 x + 6 y

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{6}{2 cos ( θ ) - 3 sin ( θ )}

Evaluate

12 = 4 x - 6 y

Move the expression to the left side

12 - 4 x + 6 y = 0

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

12 - 4 cos (θ) \times r + 6 sin (θ) \times r = 0

Factor the expression

(- 4 cos (θ) + 6 sin (θ)) r + 12 = 0

Subtract the terms

(- 4 cos (θ) + 6 sin (θ)) r + 12 - 12 = 0 - 12

Evaluate

(- 4 cos (θ) + 6 sin (θ)) r = - 12

Solution

r = \frac{6}{2 cos ( θ ) - 3 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{2}{3}

Calculate

12 = 4 x - 6 y

Take the derivative of both sides

\frac{d}{d x} (12) = \frac{d}{d x} (4 x - 6 y)

Calculate the derivative

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

4 \times 1

Any expression multiplied by 1 remains the same

4

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

4 - 6 \frac{d y}{d x}

0 = 4 - 6 \frac{d y}{d x}

Swap the sides of the equation

4 - 6 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

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

Divide the numbers

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

Solution

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

12 = 4 x - 6 y

Take the derivative of both sides

\frac{d}{d x} (12) = \frac{d}{d x} (4 x - 6 y)

Calculate the derivative

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

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

4 \times 1

Any expression multiplied by 1 remains the same

4

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

4 - 6 \frac{d y}{d x}

0 = 4 - 6 \frac{d y}{d x}

Swap the sides of the equation

4 - 6 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

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

Divide the numbers

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

Cancel out the common factor 2

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

Take the derivative of both sides

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

Calculate the derivative

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