Solve -9=-4x-7y - ScanMath

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{9}{4}

Evaluate

- 9 = - 4 x - 7 y

To find the x -intercept,set y =0

- 9 = - 4 x - 7 \times 0

Any expression multiplied by 0 equals 0

- 9 = - 4 x - 0

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

- 9 = - 4 x

Swap the sides of the equation

- 4 x = - 9

Change the signs on both sides of the equation

4 x = 9

Divide both sides

\frac{4 x}{4} = \frac{9}{4}

Solution

x = \frac{9}{4}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{9 - 7 y}{4}

Evaluate

- 9 = - 4 x - 7 y

Swap the sides of the equation

- 4 x - 7 y = - 9

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

- 4 x = - 9 + 7 y

Change the signs on both sides of the equation

4 x = 9 - 7 y

Divide both sides

\frac{4 x}{4} = \frac{9 - 7 y}{4}

Solution

x = \frac{9 - 7 y}{4}

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

- 9 = - 4 x - 7 y

To test if the graph of - 9 = - 4 x - 7 y is symmetry with respect to the origin,substitute -x for x and -y for y

- 9 = - 4 (- x) - 7 (- y)

Evaluate

More Steps

Evaluate

- 4 (- x) - 7 (- y)

Multiply the numbers

4 x - 7 (- y)

Multiply the numbers

4 x - (- 7 y)

Rewrite the expression

4 x + 7 y

- 9 = 4 x + 7 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{9}{4 cos ( θ ) + 7 sin ( θ )}

Evaluate

- 9 = - 4 x - 7 y

Move the expression to the left side

- 9 + 4 x + 7 y = 0

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

- 9 + 4 cos (θ) \times r + 7 sin (θ) \times r = 0

Factor the expression

(4 cos (θ) + 7 sin (θ)) r - 9 = 0

Subtract the terms

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

Evaluate

(4 cos (θ) + 7 sin (θ)) r = 9

Solution

r = \frac{9}{4 cos ( θ ) + 7 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{4}{7}

Calculate

- 9 = - 4 x - 7 y

Take the derivative of both sides

\frac{d}{d x} (- 9) = \frac{d}{d x} (- 4 x - 7 y)

Calculate the derivative

0 = \frac{d}{d x} (- 4 x - 7 y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 x - 7 y)

Use differentiation rules

\frac{d}{d x} (- 4 x) + \frac{d}{d x} (- 7 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 x)

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

- 4 \times \frac{d}{d x} (x)

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

- 4 \times 1

Any expression multiplied by 1 remains the same

- 4

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

- 4 - 7 \frac{d y}{d x}

0 = - 4 - 7 \frac{d y}{d x}

Swap the sides of the equation

- 4 - 7 \frac{d y}{d x} = 0

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

- 7 \frac{d y}{d x} = 0 + 4

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

- 7 \frac{d y}{d x} = 4

Change the signs on both sides of the equation

7 \frac{d y}{d x} = - 4

Divide both sides

\frac{7 \frac{d y}{d x}}{7} = \frac{- 4}{7}

Divide the numbers

\frac{d y}{d x} = \frac{- 4}{7}

Solution

\frac{d y}{d x} = - \frac{4}{7}

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

- 9 = - 4 x - 7 y

Take the derivative of both sides

\frac{d}{d x} (- 9) = \frac{d}{d x} (- 4 x - 7 y)

Calculate the derivative

0 = \frac{d}{d x} (- 4 x - 7 y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 x - 7 y)

Use differentiation rules

\frac{d}{d x} (- 4 x) + \frac{d}{d x} (- 7 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 4 x)

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

- 4 \times \frac{d}{d x} (x)

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

- 4 \times 1

Any expression multiplied by 1 remains the same

- 4

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

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

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

- 4 - 7 \frac{d y}{d x}

0 = - 4 - 7 \frac{d y}{d x}

Swap the sides of the equation

- 4 - 7 \frac{d y}{d x} = 0

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

- 7 \frac{d y}{d x} = 0 + 4

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

- 7 \frac{d y}{d x} = 4

Change the signs on both sides of the equation

7 \frac{d y}{d x} = - 4

Divide both sides

\frac{7 \frac{d y}{d x}}{7} = \frac{- 4}{7}

Divide the numbers

\frac{d y}{d x} = \frac{- 4}{7}

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

\frac{d y}{d x} = - \frac{4}{7}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- \frac{4}{7})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- \frac{4}{7})

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