Solve x+y=8 - UpStudy

Question

x + y = 8

Function

$Find the x -intercept/zero$
Find the y-intercept
Find the slope

x = 8

Evaluate

x + y = 8

To find the x -intercept,set y =0

x + 0 = 8

Solution

x = 8

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Solve the equation

$Solve for x$
$Solve for y$

x = 8 - y

Evaluate

x + y = 8

Solution

x = 8 - y

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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

x + y = 8

To test if the graph of x + y = 8 is symmetry with respect to the origin,substitute -x for x and -y for y

- x - y = 8

Solution

Not symmetry with respect to the origin

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Rewrite the equation

Rewrite in polar form
Rewrite in slope-intercept form

r = \frac{8}{c o s ( θ ) + s i n ( θ )}

Evaluate

x + y = 8

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

cos (θ) \times r + sin (θ) \times r = 8

Factor the expression

(cos (θ) + sin (θ)) r = 8

Solution

r = \frac{8}{c o s ( θ ) + s i n ( 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} = - 1

Calculate

x + y = 8

Take the derivative of both sides

\frac{d}{d x} (x + y) = \frac{d}{d x} (8)

Calculate the derivative

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Evaluate

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

Use differentiation rules

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

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

1 + \frac{d}{d x} (y)

Evaluate the derivative

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Evaluate

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

Use differentiation rules

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

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

\frac{d y}{d x}

1 + \frac{d y}{d x}

1 + \frac{d y}{d x} = \frac{d}{d x} (8)

Calculate the derivative

1 + \frac{d y}{d x} = 0

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

\frac{d y}{d x} = 0 - 1

Solution

\frac{d y}{d x} = - 1

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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

x + y = 8

Take the derivative of both sides

\frac{d}{d x} (x + y) = \frac{d}{d x} (8)

Calculate the derivative

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Evaluate

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

Use differentiation rules

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

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

1 + \frac{d}{d x} (y)

Evaluate the derivative

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Evaluate

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

Use differentiation rules

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

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

\frac{d y}{d x}

1 + \frac{d y}{d x}

1 + \frac{d y}{d x} = \frac{d}{d x} (8)

Calculate the derivative

1 + \frac{d y}{d x} = 0

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

\frac{d y}{d x} = 0 - 1

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

\frac{d y}{d x} = - 1

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (- 1)

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 1)

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

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Graph