Solve 2x + 1/4 * y = 11/4

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{11}{8}

Evaluate

2 x + \frac{1}{4} y = \frac{11}{4}

To find the x -intercept,set y =0

2 x + \frac{1}{4} \times 0 = \frac{11}{4}

Any expression multiplied by 0 equals 0

2 x + 0 = \frac{11}{4}

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

2 x = \frac{11}{4}

Multiply by the reciprocal

2 x \times \frac{1}{2} = \frac{11}{4} \times \frac{1}{2}

Multiply

x = \frac{11}{4} \times \frac{1}{2}

Solution

More Steps

Evaluate

\frac{11}{4} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{11}{4 \times 2}

Multiply the numbers

\frac{11}{8}

x = \frac{11}{8}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{11 - y}{8}

Evaluate

2 x + \frac{1}{4} y = \frac{11}{4}

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

2 x = \frac{11}{4} - \frac{1}{4} y

Divide both sides

\frac{2 x}{2} = \frac{\frac{11}{4} - \frac{1}{4} y}{2}

Divide the numbers

x = \frac{\frac{11}{4} - \frac{1}{4} y}{2}

Solution

More Steps

Evaluate

\frac{\frac{11}{4} - \frac{1}{4} y}{2}

Rewrite the expression

\frac{\frac{11 - y}{4}}{2}

Multiply by the reciprocal

\frac{11 - y}{4} \times \frac{1}{2}

To multiply the fractions,multiply the numerators and denominators separately

\frac{11 - y}{4 \times 2}

Multiply the numbers

\frac{11 - y}{8}

x = \frac{11 - y}{8}

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

2 x + \frac{1}{4} \cdot y = \frac{11}{4}

To test if the graph of 2 x + \frac{1}{4} y = \frac{11}{4} is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- x) + \frac{1}{4} (- y) = \frac{11}{4}

Evaluate

More Steps

Evaluate

2 (- x) + \frac{1}{4} (- y)

Multiply the numbers

- 2 x + \frac{1}{4} (- y)

Multiplying or dividing an odd number of negative terms equals a negative

- 2 x - \frac{1}{4} y

- 2 x - \frac{1}{4} y = \frac{11}{4}

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{11}{8 cos ( θ ) + sin ( θ )}

Evaluate

2 x + \frac{1}{4} y = \frac{11}{4}

Multiply both sides of the equation by LCD

(2 x + \frac{1}{4} y) \times 4 = \frac{11}{4} \times 4

Simplify the equation

More Steps

Evaluate

(2 x + \frac{1}{4} y) \times 4

Apply the distributive property

2 x \times 4 + \frac{1}{4} y \times 4

Simplify

2 x \times 4 + y

Multiply the numbers

8 x + y

8 x + y = \frac{11}{4} \times 4

Simplify the equation

8 x + y = 11

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

8 cos (θ) \times r + sin (θ) \times r = 11

Factor the expression

(8 cos (θ) + sin (θ)) r = 11

Solution

r = \frac{11}{8 cos ( θ ) + 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} = - 8

Calculate

2 x + \frac{1}{4} \cdot y = \frac{11}{4}

Take the derivative of both sides

\frac{d}{d x} (2 x + \frac{1}{4} y) = \frac{d}{d x} (\frac{11}{4})

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 x + \frac{1}{4} y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{1}{4} y)

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} (\frac{1}{4} y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{1}{4} y)

Use differentiation rules

\frac{d}{d y} (\frac{1}{4} y) \times \frac{d y}{d x}

Evaluate the derivative

\frac{1}{4} \frac{d y}{d x}

2 + \frac{1}{4} \frac{d y}{d x}

2 + \frac{1}{4} \frac{d y}{d x} = \frac{d}{d x} (\frac{11}{4})

Calculate the derivative

2 + \frac{1}{4} \frac{d y}{d x} = 0

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

\frac{1}{4} \frac{d y}{d x} = 0 - 2

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

\frac{1}{4} \frac{d y}{d x} = - 2

Multiply by the reciprocal

\frac{1}{4} \frac{d y}{d x} \times 4 = - 2 \times 4

Multiply

\frac{d y}{d x} = - 2 \times 4

Solution

\frac{d y}{d x} = - 8

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 + \frac{1}{4} \cdot y = \frac{11}{4}

Take the derivative of both sides

\frac{d}{d x} (2 x + \frac{1}{4} y) = \frac{d}{d x} (\frac{11}{4})

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (2 x + \frac{1}{4} y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{1}{4} y)

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} (\frac{1}{4} y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{1}{4} y)

Use differentiation rules

\frac{d}{d y} (\frac{1}{4} y) \times \frac{d y}{d x}

Evaluate the derivative

\frac{1}{4} \frac{d y}{d x}

2 + \frac{1}{4} \frac{d y}{d x}

2 + \frac{1}{4} \frac{d y}{d x} = \frac{d}{d x} (\frac{11}{4})

Calculate the derivative

2 + \frac{1}{4} \frac{d y}{d x} = 0

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

\frac{1}{4} \frac{d y}{d x} = 0 - 2

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

\frac{1}{4} \frac{d y}{d x} = - 2

Multiply by the reciprocal

\frac{1}{4} \frac{d y}{d x} \times 4 = - 2 \times 4

Multiply

\frac{d y}{d x} = - 2 \times 4

Multiply

\frac{d y}{d x} = - 8

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 8)

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