Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
2y=4x×1
To find the x-intercept,set y=0
2×0=4x×1
Any expression multiplied by 0 equals 0
0=4x×1
Multiply the terms
0=4x
Swap the sides of the equation
4x=0
Solution
x=0
Show Solution

Solve the equation
Solve for x
Solve for y
x=2y
Evaluate
2y=4x×1
Multiply the terms
2y=4x
Swap the sides of the equation
4x=2y
Divide both sides
44x=42y
Divide the numbers
x=42y
Solution
x=2y
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
Symmetry with respect to the origin
Evaluate
2y=4x1
Simplify the expression
2y=4x
To test if the graph of 2y=4x is symmetry with respect to the origin,substitute -x for x and -y for y
2(−y)=4(−x)
Evaluate
−2y=4(−x)
Evaluate
−2y=−4x
Solution
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=0θ=arccot(21)+kπ,k∈Z
Evaluate
2y=4x×1
Evaluate
2y=4x
Move the expression to the left side
2y−4x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2sin(θ)×r−4cos(θ)×r=0
Factor the expression
(2sin(θ)−4cos(θ))r=0
Separate into possible cases
r=02sin(θ)−4cos(θ)=0
Solution
More Steps

Evaluate
2sin(θ)−4cos(θ)=0
Move the expression to the right side
−4cos(θ)=0−2sin(θ)
Subtract the terms
−4cos(θ)=−2sin(θ)
Divide both sides
sin(θ)−4cos(θ)=−2
Divide the terms
More Steps

Evaluate
sin(θ)−4cos(θ)
Use b−a=−ba=−ba to rewrite the fraction
−sin(θ)4cos(θ)
Rewrite the expression
−4sin−1(θ)cos(θ)
Rewrite the expression
−4cot(θ)
−4cot(θ)=−2
Multiply both sides of the equation by −41
−4cot(θ)(−41)=−2(−41)
Calculate
cot(θ)=−2(−41)
Calculate
More Steps

Evaluate
−2(−41)
Multiplying or dividing an even number of negative terms equals a positive
2×41
Reduce the numbers
1×21
Multiply the numbers
21
cot(θ)=21
Use the inverse trigonometric function
θ=arccot(21)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(21)+kπ,k∈Z
r=0θ=arccot(21)+kπ,k∈Z
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=2
Calculate
2y=4x1
Simplify the expression
2y=4x
Take the derivative of both sides
dxd(2y)=dxd(4x)
Calculate the derivative
More Steps

Evaluate
dxd(2y)
Use differentiation rules
dyd(2y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(2y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dyd(y)
Use dxdxn=nxn−1 to find derivative
2×1
Any expression multiplied by 1 remains the same
2
2dxdy
2dxdy=dxd(4x)
Calculate the derivative
More Steps

Evaluate
dxd(4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x)
Use dxdxn=nxn−1 to find derivative
4×1
Any expression multiplied by 1 remains the same
4
2dxdy=4
Divide both sides
22dxdy=24
Divide the numbers
dxdy=24
Solution
More Steps

Evaluate
24
Reduce the numbers
12
Calculate
2
dxdy=2
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=0
Calculate
2y=4x1
Simplify the expression
2y=4x
Take the derivative of both sides
dxd(2y)=dxd(4x)
Calculate the derivative
More Steps

Evaluate
dxd(2y)
Use differentiation rules
dyd(2y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(2y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
2×dyd(y)
Use dxdxn=nxn−1 to find derivative
2×1
Any expression multiplied by 1 remains the same
2
2dxdy
2dxdy=dxd(4x)
Calculate the derivative
More Steps

Evaluate
dxd(4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x)
Use dxdxn=nxn−1 to find derivative
4×1
Any expression multiplied by 1 remains the same
4
2dxdy=4
Divide both sides
22dxdy=24
Divide the numbers
dxdy=24
Divide the numbers
More Steps

Evaluate
24
Reduce the numbers
12
Calculate
2
dxdy=2
Take the derivative of both sides
dxd(dxdy)=dxd(2)
Calculate the derivative
dx2d2y=dxd(2)
Solution
dx2d2y=0
Show Solution
