Solve 7x + 6y - 9 = 0

Question

7 x + 6 y - 9 = 0

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{9}{7}

Evaluate

7 x + 6 y - 9 = 0

To find the x -intercept,set y =0

7 x + 6 \times 0 - 9 = 0

Any expression multiplied by 0 equals 0

7 x + 0 - 9 = 0

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

7 x - 9 = 0

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

7 x = 0 + 9

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

7 x = 9

Divide both sides

\frac{7 x}{7} = \frac{9}{7}

Solution

x = \frac{9}{7}

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Solve the equation

Solve for x

Solve for y

x = \frac{- 6 y + 9}{7}

Evaluate

7 x + 6 y - 9 = 0

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

7 x = 0 - (6 y - 9)

Subtract the terms

More Steps

Evaluate

0 - (6 y - 9)

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 - 6 y + 9

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

- 6 y + 9

7 x = - 6 y + 9

Divide both sides

\frac{7 x}{7} = \frac{- 6 y + 9}{7}

Solution

x = \frac{- 6 y + 9}{7}

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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

7 x + 6 y - 9 = 0

To test if the graph of 7 x + 6 y - 9 = 0 is symmetry with respect to the origin,substitute -x for x and -y for y

7 (- x) + 6 (- y) - 9 = 0

Evaluate

More Steps

Evaluate

7 (- x) + 6 (- y) - 9

Multiply the numbers

- 7 x + 6 (- y) - 9

Multiply the numbers

- 7 x - 6 y - 9

- 7 x - 6 y - 9 = 0

Solution

Not symmetry with respect to the origin

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Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = \frac{9}{7 cos ( θ ) + 6 sin ( θ )}

Evaluate

7 x + 6 y - 9 = 0

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

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

Factor the expression

(7 cos (θ) + 6 sin (θ)) r - 9 = 0

Subtract the terms

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

Evaluate

(7 cos (θ) + 6 sin (θ)) r = 9

Solution

r = \frac{9}{7 cos ( θ ) + 6 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{7}{6}

Calculate

7 x + 6 y - 9 = 0

Take the derivative of both sides

\frac{d}{d x} (7 x + 6 y - 9) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (7 x + 6 y - 9)

Use differentiation rules

\frac{d}{d x} (7 x) + \frac{d}{d x} (6 y) + \frac{d}{d x} (- 9)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (7 x)

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

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

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

7 \times 1

Any expression multiplied by 1 remains the same

7

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

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}

7 + 6 \frac{d y}{d x} + \frac{d}{d x} (- 9)

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

7 + 6 \frac{d y}{d x} + 0

Evaluate

7 + 6 \frac{d y}{d x}

7 + 6 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

7 + 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 - 7

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

6 \frac{d y}{d x} = - 7

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{- 7}{6}

Divide the numbers

\frac{d y}{d x} = \frac{- 7}{6}

Solution

\frac{d y}{d x} = - \frac{7}{6}

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

7 x + 6 y - 9 = 0

Take the derivative of both sides

\frac{d}{d x} (7 x + 6 y - 9) = \frac{d}{d x} (0)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (7 x + 6 y - 9)

Use differentiation rules

\frac{d}{d x} (7 x) + \frac{d}{d x} (6 y) + \frac{d}{d x} (- 9)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (7 x)

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

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

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

7 \times 1

Any expression multiplied by 1 remains the same

7

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

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}

7 + 6 \frac{d y}{d x} + \frac{d}{d x} (- 9)

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

7 + 6 \frac{d y}{d x} + 0

Evaluate

7 + 6 \frac{d y}{d x}

7 + 6 \frac{d y}{d x} = \frac{d}{d x} (0)

Calculate the derivative

7 + 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 - 7

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

6 \frac{d y}{d x} = - 7

Divide both sides

\frac{6 \frac{d y}{d x}}{6} = \frac{- 7}{6}

Divide the numbers

\frac{d y}{d x} = \frac{- 7}{6}

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

\frac{d y}{d x} = - \frac{7}{6}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{7}{6})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{7}{6})

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