Solve 3/4x - 5y = 7

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = \frac{28}{3}

Evaluate

\frac{3}{4} x - 5 y = 7

To find the x -intercept,set y =0

\frac{3}{4} x - 5 \times 0 = 7

Any expression multiplied by 0 equals 0

\frac{3}{4} x - 0 = 7

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

\frac{3}{4} x = 7

Multiply by the reciprocal

\frac{3}{4} x \times \frac{4}{3} = 7 \times \frac{4}{3}

Multiply

x = 7 \times \frac{4}{3}

Solution

More Steps

Evaluate

7 \times \frac{4}{3}

Multiply the numbers

\frac{7 \times 4}{3}

Multiply the numbers

\frac{28}{3}

x = \frac{28}{3}

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{28 + 20 y}{3}

Evaluate

\frac{3}{4} x - 5 y = 7

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

\frac{3}{4} x = 7 + 5 y

Multiply by the reciprocal

\frac{3}{4} x \times \frac{4}{3} = (7 + 5 y) \times \frac{4}{3}

Multiply

x = (7 + 5 y) \times \frac{4}{3}

Solution

More Steps

Evaluate

(7 + 5 y) \times \frac{4}{3}

Multiply the numbers

\frac{( 7 + 5 y ) \times 4}{3}

Multiply the numbers

More Steps

Evaluate

(7 + 5 y) \times 4

Apply the distributive property

7 \times 4 + 5 y \times 4

Multiply the numbers

28 + 5 y \times 4

Multiply the terms

28 + 20 y

\frac{28 + 20 y}{3}

x = \frac{28 + 20 y}{3}

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

\frac{3}{4} x - 5 y = 7

To test if the graph of \frac{3}{4} x - 5 y = 7 is symmetry with respect to the origin,substitute -x for x and -y for y

\frac{3}{4} (- x) - 5 (- y) = 7

Evaluate

More Steps

Evaluate

\frac{3}{4} (- x) - 5 (- y)

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

- \frac{3}{4} x - 5 (- y)

Multiply the numbers

- \frac{3}{4} x - (- 5 y)

Rewrite the expression

- \frac{3}{4} x + 5 y

- \frac{3}{4} x + 5 y = 7

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{28}{3 cos ( θ ) - 20 sin ( θ )}

Evaluate

\frac{3}{4} x - 5 y = 7

Multiply both sides of the equation by LCD

(\frac{3}{4} x - 5 y) \times 4 = 7 \times 4

Simplify the equation

More Steps

Evaluate

(\frac{3}{4} x - 5 y) \times 4

Apply the distributive property

\frac{3}{4} x \times 4 - 5 y \times 4

Simplify

3 x - 5 y \times 4

Multiply the numbers

3 x - 20 y

3 x - 20 y = 7 \times 4

Simplify the equation

3 x - 20 y = 28

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

3 cos (θ) \times r - 20 sin (θ) \times r = 28

Factor the expression

(3 cos (θ) - 20 sin (θ)) r = 28

Solution

r = \frac{28}{3 cos ( θ ) - 20 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{3}{20}

Calculate

\frac{3}{4} x - 5 y = 7

Take the derivative of both sides

\frac{d}{d x} (\frac{3}{4} x - 5 y) = \frac{d}{d x} (7)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3}{4} x - 5 y)

Use differentiation rules

\frac{d}{d x} (\frac{3}{4} x) + \frac{d}{d x} (- 5 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3}{4} x)

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

\frac{3}{4} \times \frac{d}{d x} (x)

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

\frac{3}{4} \times 1

Any expression multiplied by 1 remains the same

\frac{3}{4}

\frac{3}{4} + \frac{d}{d x} (- 5 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 5 y)

Use differentiation rules

\frac{d}{d y} (- 5 y) \times \frac{d y}{d x}

Evaluate the derivative

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

\frac{3}{4} - 5 \frac{d y}{d x}

\frac{3}{4} - 5 \frac{d y}{d x} = \frac{d}{d x} (7)

Calculate the derivative

\frac{3}{4} - 5 \frac{d y}{d x} = 0

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

- 5 \frac{d y}{d x} = 0 - \frac{3}{4}

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

- 5 \frac{d y}{d x} = - \frac{3}{4}

Change the signs on both sides of the equation

5 \frac{d y}{d x} = \frac{3}{4}

Multiply by the reciprocal

5 \frac{d y}{d x} \times \frac{1}{5} = \frac{3}{4} \times \frac{1}{5}

Multiply

\frac{d y}{d x} = \frac{3}{4} \times \frac{1}{5}

Solution

More Steps

Evaluate

\frac{3}{4} \times \frac{1}{5}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{4 \times 5}

Multiply the numbers

\frac{3}{20}

\frac{d y}{d x} = \frac{3}{20}

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

\frac{3}{4} x - 5 y = 7

Take the derivative of both sides

\frac{d}{d x} (\frac{3}{4} x - 5 y) = \frac{d}{d x} (7)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3}{4} x - 5 y)

Use differentiation rules

\frac{d}{d x} (\frac{3}{4} x) + \frac{d}{d x} (- 5 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{3}{4} x)

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

\frac{3}{4} \times \frac{d}{d x} (x)

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

\frac{3}{4} \times 1

Any expression multiplied by 1 remains the same

\frac{3}{4}

\frac{3}{4} + \frac{d}{d x} (- 5 y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 5 y)

Use differentiation rules

\frac{d}{d y} (- 5 y) \times \frac{d y}{d x}

Evaluate the derivative

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

\frac{3}{4} - 5 \frac{d y}{d x}

\frac{3}{4} - 5 \frac{d y}{d x} = \frac{d}{d x} (7)

Calculate the derivative

\frac{3}{4} - 5 \frac{d y}{d x} = 0

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

- 5 \frac{d y}{d x} = 0 - \frac{3}{4}

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

- 5 \frac{d y}{d x} = - \frac{3}{4}

Change the signs on both sides of the equation

5 \frac{d y}{d x} = \frac{3}{4}

Multiply by the reciprocal

5 \frac{d y}{d x} \times \frac{1}{5} = \frac{3}{4} \times \frac{1}{5}

Multiply

\frac{d y}{d x} = \frac{3}{4} \times \frac{1}{5}

Multiply

More Steps

Evaluate

\frac{3}{4} \times \frac{1}{5}

To multiply the fractions,multiply the numerators and denominators separately

\frac{3}{4 \times 5}

Multiply the numbers

\frac{3}{20}

\frac{d y}{d x} = \frac{3}{20}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{3}{20})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{3}{20})

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