Solve 2x + 3y + 5 = 0

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = - \frac{5}{2}

Evaluate

2 x + 3 y + 5 = 0

To find the x -intercept,set y =0

2 x + 3 \times 0 + 5 = 0

Any expression multiplied by 0 equals 0

2 x + 0 + 5 = 0

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

2 x + 5 = 0

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

2 x = 0 - 5

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

2 x = - 5

Divide both sides

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

Divide the numbers

x = \frac{- 5}{2}

Solution

x = - \frac{5}{2}

Show Solution

Solve the equation

Solve for x

Solve for y

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

Evaluate

2 x + 3 y + 5 = 0

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

2 x = 0 - (3 y + 5)

Subtract the terms

More Steps

Evaluate

0 - (3 y + 5)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

0 - 3 y - 5

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

- 3 y - 5

2 x = - 3 y - 5

Divide both sides

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

Divide the numbers

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

Solution

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

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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

2 x + 3 y + 5 = 0

To test if the graph of 2 x + 3 y + 5 = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- x) + 3 (- y) + 5 = 0

Evaluate

More Steps

Evaluate

2 (- x) + 3 (- y) + 5

Multiply the numbers

- 2 x + 3 (- y) + 5

Multiply the numbers

- 2 x - 3 y + 5

- 2 x - 3 y + 5 = 0

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{5}{2 cos ( θ ) + 3 sin ( θ )}

Evaluate

2 x + 3 y + 5 = 0

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

2 cos (θ) \times r + 3 sin (θ) \times r + 5 = 0

Factor the expression

(2 cos (θ) + 3 sin (θ)) r + 5 = 0

Subtract the terms

(2 cos (θ) + 3 sin (θ)) r + 5 - 5 = 0 - 5

Evaluate

(2 cos (θ) + 3 sin (θ)) r = - 5

Solution

r = - \frac{5}{2 cos ( θ ) + 3 sin ( θ )}

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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

2 x + 3 y + 5 = 0

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y + 5) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

2 \times 1

Any expression multiplied by 1 remains the same

2

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

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}

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

Use \frac{d}{d x} (c) = 0 to find derivative

2 + 3 \frac{d y}{d x} + 0

Evaluate

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

2 + 3 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

2 + 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 - 2

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

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

Divide both sides

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

Divide the numbers

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

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

2 x + 3 y + 5 = 0

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y + 5) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

2 \times 1

Any expression multiplied by 1 remains the same

2

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

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}

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

Use \frac{d}{d x} (c) = 0 to find derivative

2 + 3 \frac{d y}{d x} + 0

Evaluate

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

2 + 3 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

2 + 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 - 2

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

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

Divide both sides

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

Divide the numbers

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

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

\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