Solve 3y - 15x = -15

Question

Function

Find the x -intercept/zero

Find the y-intercept

Find the slope

x = 1

Evaluate

3 y - 15 x = - 15

To find the x -intercept,set y =0

3 \times 0 - 15 x = - 15

Any expression multiplied by 0 equals 0

0 - 15 x = - 15

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

- 15 x = - 15

Change the signs on both sides of the equation

15 x = 15

Divide both sides

\frac{15 x}{15} = \frac{15}{15}

Divide the numbers

x = \frac{15}{15}

Solution

More Steps

Evaluate

\frac{15}{15}

Reduce the numbers

\frac{1}{1}

Calculate

1

x = 1

Show Solution

Solve the equation

Solve for x

Solve for y

x = \frac{5 + y}{5}

Evaluate

3 y - 15 x = - 15

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

- 15 x = - 15 - 3 y

Change the signs on both sides of the equation

15 x = 15 + 3 y

Divide both sides

\frac{15 x}{15} = \frac{15 + 3 y}{15}

Divide the numbers

x = \frac{15 + 3 y}{15}

Solution

More Steps

Evaluate

\frac{15 + 3 y}{15}

Rewrite the expression

\frac{3 ( 5 + y )}{15}

Cancel out the common factor 3

\frac{5 + y}{5}

x = \frac{5 + y}{5}

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

3 y - 15 x = - 15

To test if the graph of 3 y - 15 x = - 15 is symmetry with respect to the origin,substitute -x for x and -y for y

3 (- y) - 15 (- x) = - 15

Evaluate

More Steps

Evaluate

3 (- y) - 15 (- x)

Multiply the numbers

- 3 y - 15 (- x)

Multiply the numbers

- 3 y - (- 15 x)

Rewrite the expression

- 3 y + 15 x

- 3 y + 15 x = - 15

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{5}{sin ( θ ) - 5 cos ( θ )}

Evaluate

3 y - 15 x = - 15

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

3 sin (θ) \times r - 15 cos (θ) \times r = - 15

Factor the expression

(3 sin (θ) - 15 cos (θ)) r = - 15

Solution

r = - \frac{5}{sin ( θ ) - 5 cos ( 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} = 5

Calculate

3 y - 15 x = - 15

Take the derivative of both sides

\frac{d}{d x} (3 y - 15 x) = \frac{d}{d x} (- 15)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 y - 15 x)

Use differentiation rules

\frac{d}{d x} (3 y) + \frac{d}{d x} (- 15 x)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

3 \frac{d y}{d x}

3 \frac{d y}{d x} + \frac{d}{d x} (- 15 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 15 x)

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

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

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

- 15 \times 1

Any expression multiplied by 1 remains the same

- 15

3 \frac{d y}{d x} - 15

3 \frac{d y}{d x} - 15 = \frac{d}{d x} (- 15)

Calculate the derivative

3 \frac{d y}{d x} - 15 = 0

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

3 \frac{d y}{d x} = 0 + 15

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

3 \frac{d y}{d x} = 15

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{15}{3}

Divide the numbers

\frac{d y}{d x} = \frac{15}{3}

Solution

More Steps

Evaluate

\frac{15}{3}

Reduce the numbers

\frac{5}{1}

Calculate

5

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

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

3 y - 15 x = - 15

Take the derivative of both sides

\frac{d}{d x} (3 y - 15 x) = \frac{d}{d x} (- 15)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 y - 15 x)

Use differentiation rules

\frac{d}{d x} (3 y) + \frac{d}{d x} (- 15 x)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

3 \frac{d y}{d x}

3 \frac{d y}{d x} + \frac{d}{d x} (- 15 x)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (- 15 x)

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

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

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

- 15 \times 1

Any expression multiplied by 1 remains the same

- 15

3 \frac{d y}{d x} - 15

3 \frac{d y}{d x} - 15 = \frac{d}{d x} (- 15)

Calculate the derivative

3 \frac{d y}{d x} - 15 = 0

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

3 \frac{d y}{d x} = 0 + 15

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

3 \frac{d y}{d x} = 15

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{15}{3}

Divide the numbers

\frac{d y}{d x} = \frac{15}{3}

Divide the numbers

More Steps

Evaluate

\frac{15}{3}

Reduce the numbers

\frac{5}{1}

Calculate

5

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

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (5)

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