Solve 3x+1/5y=7 - ScanMath

Question

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

x = \frac{7}{3}

Evaluate

3 x + \frac{1}{5} y = 7

To find the x -intercept,set y =0

3 x + \frac{1}{5} \times 0 = 7

Any expression multiplied by 0 equals 0

3 x + 0 = 7

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

3 x = 7

Divide both sides

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

Solution

x = \frac{7}{3}

Show Solution

Solve the equation

$Solve for x$

$Solve for y$

x = \frac{35 - y}{15}

Evaluate

3 x + \frac{1}{5} y = 7

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

3 x = 7 - \frac{1}{5} y

Divide both sides

\frac{3 x}{3} = \frac{7 - \frac{1}{5} y}{3}

Divide the numbers

x = \frac{7 - \frac{1}{5} y}{3}

Solution

More Steps

Evaluate

\frac{7 - \frac{1}{5} y}{3}

Rewrite the expression

\frac{\frac{35 - y}{5}}{3}

Multiply by the reciprocal

\frac{35 - y}{5} \times \frac{1}{3}

To multiply the fractions,multiply the numerators and denominators separately

\frac{35 - y}{5 \times 3}

Multiply the numbers

\frac{35 - y}{15}

x = \frac{35 - y}{15}

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 x + \frac{1}{5} y = 7

To test if the graph of 3 x + \frac{1}{5} y = 7 is symmetry with respect to the origin,substitute -x for x and -y for y

3 (- x) + \frac{1}{5} (- y) = 7

Evaluate

More Steps

Evaluate

3 (- x) + \frac{1}{5} (- y)

Multiply the numbers

- 3 x + \frac{1}{5} (- y)

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

- 3 x - \frac{1}{5} y

- 3 x - \frac{1}{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{35}{15 cos ( θ ) + sin ( θ )}

Evaluate

3 x + \frac{1}{5} y = 7

Multiply both sides of the equation by LCD

(3 x + \frac{1}{5} y) \times 5 = 7 \times 5

Simplify the equation

More Steps

Evaluate

(3 x + \frac{1}{5} y) \times 5

Apply the distributive property

3 x \times 5 + \frac{1}{5} y \times 5

Simplify

3 x \times 5 + y

Multiply the numbers

15 x + y

15 x + y = 7 \times 5

Simplify the equation

15 x + y = 35

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

15 cos (θ) \times r + sin (θ) \times r = 35

Factor the expression

(15 cos (θ) + sin (θ)) r = 35

Solution

r = \frac{35}{15 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} = - 15

Calculate

3 x + \frac{1}{5} y = 7

Take the derivative of both sides

\frac{d}{d x} (3 x + \frac{1}{5} y) = \frac{d}{d x} (7)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x + \frac{1}{5} y)

Use differentiation rules

\frac{d}{d x} (3 x) + \frac{d}{d x} (\frac{1}{5} y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

3 \times 1

Any expression multiplied by 1 remains the same

3

3 + \frac{d}{d x} (\frac{1}{5} y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{1}{5} y)

Use differentiation rules

\frac{d}{d y} (\frac{1}{5} y) \times \frac{d y}{d x}

Evaluate the derivative

\frac{1}{5} \frac{d y}{d x}

3 + \frac{1}{5} \frac{d y}{d x}

3 + \frac{1}{5} \frac{d y}{d x} = \frac{d}{d x} (7)

Calculate the derivative

3 + \frac{1}{5} \frac{d y}{d x} = 0

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

\frac{1}{5} \frac{d y}{d x} = 0 - 3

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

\frac{1}{5} \frac{d y}{d x} = - 3

Multiply by the reciprocal

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

Multiply

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

Solution

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

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 x + \frac{1}{5} y = 7

Take the derivative of both sides

\frac{d}{d x} (3 x + \frac{1}{5} y) = \frac{d}{d x} (7)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (3 x + \frac{1}{5} y)

Use differentiation rules

\frac{d}{d x} (3 x) + \frac{d}{d x} (\frac{1}{5} y)

Evaluate the derivative

More Steps

Evaluate

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

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

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

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

3 \times 1

Any expression multiplied by 1 remains the same

3

3 + \frac{d}{d x} (\frac{1}{5} y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (\frac{1}{5} y)

Use differentiation rules

\frac{d}{d y} (\frac{1}{5} y) \times \frac{d y}{d x}

Evaluate the derivative

\frac{1}{5} \frac{d y}{d x}

3 + \frac{1}{5} \frac{d y}{d x}

3 + \frac{1}{5} \frac{d y}{d x} = \frac{d}{d x} (7)

Calculate the derivative

3 + \frac{1}{5} \frac{d y}{d x} = 0

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

\frac{1}{5} \frac{d y}{d x} = 0 - 3

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

\frac{1}{5} \frac{d y}{d x} = - 3

Multiply by the reciprocal

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

Multiply

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

Multiply

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

Take the derivative of both sides

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

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (- 15)

Solution

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

Show Solution

3x+1/5y=7

Function

Find the x-intercept/zero

Find the y-intercept

Find the slope

Solve the equation

Solve for x

Solve for y

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

Graph

$Find the x -intercept/zero$

$Solve for x$

$Solve for y$

$Find the derivative with respect to x$

$Find the derivative with respect to y$

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$