Solve 6x-3y = 18 - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 3

Evaluate

6 x - 3 y = 18

To find the x -intercept,set y =0

6 x - 3 \times 0 = 18

Any expression multiplied by 0 equals 0

6 x - 0 = 18

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

6 x = 18

Divide both sides

\frac{6 x}{6} = \frac{18}{6}

Divide the numbers

x = \frac{18}{6}

Solution

More Steps

Evaluate

\frac{18}{6}

Reduce the numbers

\frac{3}{1}

Calculate

3

x = 3

Show Solution

Solve the equation

Solve for x

Solve for y

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

Evaluate

6 x - 3 y = 18

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

6 x = 18 + 3 y

Divide both sides

\frac{6 x}{6} = \frac{18 + 3 y}{6}

Divide the numbers

x = \frac{18 + 3 y}{6}

Solution

More Steps

Evaluate

\frac{18 + 3 y}{6}

Rewrite the expression

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

Cancel out the common factor 3

\frac{6 + y}{2}

x = \frac{6 + 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

6 x - 3 y = 18

To test if the graph of 6 x - 3 y = 18 is symmetry with respect to the origin,substitute -x for x and -y for y

6 (- x) - 3 (- y) = 18

Evaluate

More Steps

Evaluate

6 (- x) - 3 (- y)

Multiply the numbers

- 6 x - 3 (- y)

Multiply the numbers

- 6 x - (- 3 y)

Rewrite the expression

- 6 x + 3 y

- 6 x + 3 y = 18

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 ) - sin ( θ )}

Evaluate

6 x - 3 y = 18

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

6 cos (θ) \times r - 3 sin (θ) \times r = 18

Factor the expression

(6 cos (θ) - 3 sin (θ)) r = 18

Solution

r = \frac{6}{2 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} = 2

Calculate

6 x - 3 y = 18

Take the derivative of both sides

\frac{d}{d x} (6 x - 3 y) = \frac{d}{d x} (18)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (6 x - 3 y)

Use differentiation rules

\frac{d}{d x} (6 x) + \frac{d}{d x} (- 3 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} (- 3 y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

6 - 3 \frac{d y}{d x}

6 - 3 \frac{d y}{d x} = \frac{d}{d x} (18)

Calculate the derivative

6 - 3 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{6}{3}

Divide the numbers

\frac{d y}{d x} = \frac{6}{3}

Solution

More Steps

Evaluate

\frac{6}{3}

Reduce the numbers

\frac{2}{1}

Calculate

2

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

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 - 3 y = 18

Take the derivative of both sides

\frac{d}{d x} (6 x - 3 y) = \frac{d}{d x} (18)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (6 x - 3 y)

Use differentiation rules

\frac{d}{d x} (6 x) + \frac{d}{d x} (- 3 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} (- 3 y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

6 - 3 \frac{d y}{d x}

6 - 3 \frac{d y}{d x} = \frac{d}{d x} (18)

Calculate the derivative

6 - 3 \frac{d y}{d x} = 0

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

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

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

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

Change the signs on both sides of the equation

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

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{6}{3}

Divide the numbers

\frac{d y}{d x} = \frac{6}{3}

Divide the numbers

More Steps

Evaluate

\frac{6}{3}

Reduce the numbers

\frac{2}{1}

Calculate

2

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

Take the derivative of both sides

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

Calculate the derivative

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

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