Solve 3x/2-5y/3=-2

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{4}{3}

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

To find the x -intercept,set y =0

(3 \times \frac{x}{2}) - (5 \times \frac{0}{3}) = - 2

Simplify

More Steps

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{0}{3})

Multiply the terms

\frac{3 x}{2} - (5 \times \frac{0}{3})

Divide the terms

\frac{3 x}{2} - (5 \times 0)

Any expression multiplied by 0 equals 0

\frac{3 x}{2} - 0

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

\frac{3 x}{2}

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

Cross multiply

3 x = 2 (- 2)

Simplify the equation

3 x = - 4

Divide both sides

\frac{3 x}{3} = \frac{- 4}{3}

Divide the numbers

x = \frac{- 4}{3}

Solution

x = - \frac{4}{3}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{- 12 + 10 y}{9}

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

Simplify

More Steps

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3})

Multiply the terms

\frac{3 x}{2} - (5 \times \frac{y}{3})

Multiply the terms

\frac{3 x}{2} - \frac{5 y}{3}

\frac{3 x}{2} - \frac{5 y}{3} = - 2

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

\frac{3 x}{2} = - 2 + \frac{5 y}{3}

Add the terms

More Steps

Evaluate

- 2 + \frac{5 y}{3}

Reduce fractions to a common denominator

- \frac{2 \times 3}{3} + \frac{5 y}{3}

Write all numerators above the common denominator

\frac{- 2 \times 3 + 5 y}{3}

Multiply the numbers

\frac{- 6 + 5 y}{3}

\frac{3 x}{2} = \frac{- 6 + 5 y}{3}

Multiply both sides of the equation by 2

\frac{3 x}{2} \times 2 = \frac{- 6 + 5 y}{3} \times 2

Multiply the terms

3 x = \frac{( - 6 + 5 y ) \times 2}{3}

Divide the terms

3 x = \frac{- 12 + 10 y}{3}

Multiply by the reciprocal

3 x \times \frac{1}{3} = \frac{- 12 + 10 y}{3} \times \frac{1}{3}

Multiply

x = \frac{- 12 + 10 y}{3} \times \frac{1}{3}

Solution

More Steps

Evaluate

\frac{- 12 + 10 y}{3} \times \frac{1}{3}

Rewrite the expression

- \frac{12 - 10 y}{3} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

- \frac{12 - 10 y}{3 \times 3}

Multiply the numbers

- \frac{12 - 10 y}{9}

Calculate the product

\frac{- 12 + 10 y}{9}

x = \frac{- 12 + 10 y}{9}

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

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

Simplify the expression

\frac{3 x}{2} - \frac{5 y}{3} = - 2

To test if the graph of \frac{3 x}{2} - \frac{5 y}{3} = - 2 is symmetry with respect to the origin,substitute -x for x and -y for y

\frac{3 ( - x )}{2} - \frac{5 ( - y )}{3} = - 2

Evaluate

More Steps

Evaluate

\frac{3 ( - x )}{2} - \frac{5 ( - y )}{3}

Multiply the numbers

\frac{- 3 x}{2} - \frac{5 ( - y )}{3}

Multiply the numbers

\frac{- 3 x}{2} - \frac{- 5 y}{3}

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

- \frac{3 x}{2} - \frac{- 5 y}{3}

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

- \frac{3 x}{2} - (- \frac{5 y}{3})

Subtract the terms

- \frac{3 x}{2} + \frac{5 y}{3}

- \frac{3 x}{2} + \frac{5 y}{3} = - 2

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{12}{9 cos ( θ ) - 10 sin ( θ )}

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

Evaluate

More Steps

Evaluate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3})

Multiply the terms

\frac{3 x}{2} - (5 \times \frac{y}{3})

Multiply the terms

\frac{3 x}{2} - \frac{5 y}{3}

\frac{3 x}{2} - \frac{5 y}{3} = - 2

Multiply both sides of the equation by LCD

(\frac{3 x}{2} - \frac{5 y}{3}) \times 6 = - 2 \times 6

Simplify the equation

More Steps

Evaluate

(\frac{3 x}{2} - \frac{5 y}{3}) \times 6

Apply the distributive property

\frac{3 x}{2} \times 6 - \frac{5 y}{3} \times 6

Simplify

3 x \times 3 - 5 y \times 2

Multiply the numbers

9 x - 5 y \times 2

Multiply the numbers

9 x - 10 y

9 x - 10 y = - 2 \times 6

Simplify the equation

9 x - 10 y = - 12

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

9 cos (θ) \times r - 10 sin (θ) \times r = - 12

Factor the expression

(9 cos (θ) - 10 sin (θ)) r = - 12

Solution

r = - \frac{12}{9 cos ( θ ) - 10 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{9}{10}

Calculate

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

Simplify the expression

\frac{3 x}{2} - \frac{5 y}{3} = - 2

Take the derivative of both sides

\frac{d}{d x} (\frac{3 x}{2} - \frac{5 y}{3}) = \frac{d}{d x} (- 2)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3 x}{2} - \frac{5 y}{3})

Use differentiation rules

\frac{d}{d x} (\frac{3 x}{2}) - \frac{d}{d x} (\frac{5 y}{3})

Evaluate the derivative

More Steps

Evaluate

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

Rewrite the expression

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

Evaluate the derivative

\frac{3}{2}

\frac{3}{2} - \frac{d}{d x} (\frac{5 y}{3})

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{5 y}{3})

Rewrite the expression

\frac{\frac{d}{d x} ( 5 y )}{3}

Evaluate the derivative

\frac{5 \frac{d y}{d x}}{3}

\frac{3}{2} - \frac{5 \frac{d y}{d x}}{3}

Calculate

\frac{9 - 10 \frac{d y}{d x}}{6}

\frac{9 - 10 \frac{d y}{d x}}{6} = \frac{d}{d x} (- 2)

Calculate the derivative

\frac{9 - 10 \frac{d y}{d x}}{6} = 0

Simplify

9 - 10 \frac{d y}{d x} = 0

Move the constant to the right side

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

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

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

Change the signs on both sides of the equation

10 \frac{d y}{d x} = 9

Divide both sides

\frac{10 \frac{d y}{d x}}{10} = \frac{9}{10}

Solution

\frac{d y}{d x} = \frac{9}{10}

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

(3 \times \frac{x}{2}) - (5 \times \frac{y}{3}) = - 2

Simplify the expression

\frac{3 x}{2} - \frac{5 y}{3} = - 2

Take the derivative of both sides

\frac{d}{d x} (\frac{3 x}{2} - \frac{5 y}{3}) = \frac{d}{d x} (- 2)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3 x}{2} - \frac{5 y}{3})

Use differentiation rules

\frac{d}{d x} (\frac{3 x}{2}) - \frac{d}{d x} (\frac{5 y}{3})

Evaluate the derivative

More Steps

Evaluate

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

Rewrite the expression

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

Evaluate the derivative

\frac{3}{2}

\frac{3}{2} - \frac{d}{d x} (\frac{5 y}{3})

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{5 y}{3})

Rewrite the expression

\frac{\frac{d}{d x} ( 5 y )}{3}

Evaluate the derivative

\frac{5 \frac{d y}{d x}}{3}

\frac{3}{2} - \frac{5 \frac{d y}{d x}}{3}

Calculate

\frac{9 - 10 \frac{d y}{d x}}{6}

\frac{9 - 10 \frac{d y}{d x}}{6} = \frac{d}{d x} (- 2)

Calculate the derivative

\frac{9 - 10 \frac{d y}{d x}}{6} = 0

Simplify

9 - 10 \frac{d y}{d x} = 0

Move the constant to the right side

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

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

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

Change the signs on both sides of the equation

10 \frac{d y}{d x} = 9

Divide both sides

\frac{10 \frac{d y}{d x}}{10} = \frac{9}{10}

Divide the numbers

\frac{d y}{d x} = \frac{9}{10}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{9}{10})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{9}{10})

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