Solve 1818=6x+9y - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 303

Evaluate

1818 = 6 x + 9 y

To find the x -intercept,set y =0

1818 = 6 x + 9 \times 0

Any expression multiplied by 0 equals 0

1818 = 6 x + 0

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

1818 = 6 x

Swap the sides of the equation

6 x = 1818

Divide both sides

\frac{6 x}{6} = \frac{1818}{6}

Divide the numbers

x = \frac{1818}{6}

Solution

More Steps

Evaluate

\frac{1818}{6}

Reduce the numbers

\frac{303}{1}

Calculate

303

x = 303

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{606 - 3 y}{2}

Evaluate

1818 = 6 x + 9 y

Swap the sides of the equation

6 x + 9 y = 1818

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

6 x = 1818 - 9 y

Divide both sides

\frac{6 x}{6} = \frac{1818 - 9 y}{6}

Divide the numbers

x = \frac{1818 - 9 y}{6}

Solution

More Steps

Evaluate

\frac{1818 - 9 y}{6}

Rewrite the expression

\frac{3 ( 606 - 3 y )}{6}

Cancel out the common factor 3

\frac{606 - 3 y}{2}

x = \frac{606 - 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

1818 = 6 x + 9 y

To test if the graph of 1818 = 6 x + 9 y is symmetry with respect to the origin,substitute -x for x and -y for y

1818 = 6 (- x) + 9 (- y)

Evaluate

More Steps

Evaluate

6 (- x) + 9 (- y)

Multiply the numbers

- 6 x + 9 (- y)

Multiply the numbers

- 6 x - 9 y

1818 = - 6 x - 9 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{606}{2 cos ( θ ) + 3 sin ( θ )}

Evaluate

1818 = 6 x + 9 y

Move the expression to the left side

1818 - 6 x - 9 y = 0

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

1818 - 6 cos (θ) \times r - 9 sin (θ) \times r = 0

Factor the expression

(- 6 cos (θ) - 9 sin (θ)) r + 1818 = 0

Subtract the terms

(- 6 cos (θ) - 9 sin (θ)) r + 1818 - 1818 = 0 - 1818

Evaluate

(- 6 cos (θ) - 9 sin (θ)) r = - 1818

Solution

r = \frac{606}{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

1818 = 6 x + 9 y

Take the derivative of both sides

\frac{d}{d x} (1818) = \frac{d}{d x} (6 x + 9 y)

Calculate the derivative

0 = \frac{d}{d x} (6 x + 9 y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (6 x + 9 y)

Use differentiation rules

\frac{d}{d x} (6 x) + \frac{d}{d x} (9 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} (9 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y)

Use differentiation rules

\frac{d}{d y} (9 y) \times \frac{d y}{d x}

Evaluate the derivative

9 \frac{d y}{d x}

6 + 9 \frac{d y}{d x}

0 = 6 + 9 \frac{d y}{d x}

Swap the sides of the equation

6 + 9 \frac{d y}{d x} = 0

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

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

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

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

Divide both sides

\frac{9 \frac{d y}{d x}}{9} = \frac{- 6}{9}

Divide the numbers

\frac{d y}{d x} = \frac{- 6}{9}

Solution

More Steps

Evaluate

\frac{- 6}{9}

Cancel out the common factor 3

\frac{- 2}{3}

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

- \frac{2}{3}

\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

1818 = 6 x + 9 y

Take the derivative of both sides

\frac{d}{d x} (1818) = \frac{d}{d x} (6 x + 9 y)

Calculate the derivative

0 = \frac{d}{d x} (6 x + 9 y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (6 x + 9 y)

Use differentiation rules

\frac{d}{d x} (6 x) + \frac{d}{d x} (9 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} (9 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (9 y)

Use differentiation rules

\frac{d}{d y} (9 y) \times \frac{d y}{d x}

Evaluate the derivative

9 \frac{d y}{d x}

6 + 9 \frac{d y}{d x}

0 = 6 + 9 \frac{d y}{d x}

Swap the sides of the equation

6 + 9 \frac{d y}{d x} = 0

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

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

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

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

Divide both sides

\frac{9 \frac{d y}{d x}}{9} = \frac{- 6}{9}

Divide the numbers

\frac{d y}{d x} = \frac{- 6}{9}

Divide the numbers

More Steps

Evaluate

\frac{- 6}{9}

Cancel out the common factor 3

\frac{- 2}{3}

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

- \frac{2}{3}

\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