Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
x×8=2y
To find the x-intercept,set y=0
x×8=2×0
Any expression multiplied by 0 equals 0
x×8=0
Use the commutative property to reorder the terms
8x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=4y
Evaluate
x×8=2y
Use the commutative property to reorder the terms
8x=2y
Divide both sides
88x=82y
Divide the numbers
x=82y
Solution
x=4y
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
x8=2y
Simplify the expression
8x=2y
To test if the graph of 8x=2y is symmetry with respect to the origin,substitute -x for x and -y for y
8(−x)=2(−y)
Evaluate
−8x=2(−y)
Evaluate
−8x=−2y
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=arctan(4)+kπ,k∈Z
Evaluate
x×8=2y
Use the commutative property to reorder the terms
8x=2y
Move the expression to the left side
8x−2y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
8cos(θ)×r−2sin(θ)×r=0
Factor the expression
(8cos(θ)−2sin(θ))r=0
Separate into possible cases
r=08cos(θ)−2sin(θ)=0
Solution
More Steps
Evaluate
8cos(θ)−2sin(θ)=0
Move the expression to the right side
−2sin(θ)=0−8cos(θ)
Subtract the terms
−2sin(θ)=−8cos(θ)
Divide both sides
cos(θ)−2sin(θ)=−8
Divide the terms
More Steps
Evaluate
cos(θ)−2sin(θ)
Use b−a=−ba=−ba to rewrite the fraction
−cos(θ)2sin(θ)
Rewrite the expression
−2cos−1(θ)sin(θ)
Rewrite the expression
−2tan(θ)
−2tan(θ)=−8
Multiply both sides of the equation by −21
−2tan(θ)(−21)=−8(−21)
Calculate
tan(θ)=−8(−21)
Calculate
More Steps
Evaluate
−8(−21)
Multiplying or dividing an even number of negative terms equals a positive
8×21
Reduce the numbers
4×1
Simplify
4
tan(θ)=4
Use the inverse trigonometric function
θ=arctan(4)
Add the period of kπ,k∈Z to find all solutions
θ=arctan(4)+kπ,k∈Z
r=0θ=arctan(4)+kπ,k∈Z
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=4
Calculate
x8=2y
Simplify the expression
8x=2y
Take the derivative of both sides
dxd(8x)=dxd(2y)
Calculate the derivative
More Steps
Evaluate
dxd(8x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
8×dxd(x)
Use dxdxn=nxn−1 to find derivative
8×1
Any expression multiplied by 1 remains the same
8
8=dxd(2y)
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
8=2dxdy
Swap the sides of the equation
2dxdy=8
Divide both sides
22dxdy=28
Divide the numbers
dxdy=28
Solution
More Steps
Evaluate
28
Reduce the numbers
14
Calculate
4
dxdy=4
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
x8=2y
Simplify the expression
8x=2y
Take the derivative of both sides
dxd(8x)=dxd(2y)
Calculate the derivative
More Steps
Evaluate
dxd(8x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
8×dxd(x)
Use dxdxn=nxn−1 to find derivative
8×1
Any expression multiplied by 1 remains the same
8
8=dxd(2y)
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
8=2dxdy
Swap the sides of the equation
2dxdy=8
Divide both sides
22dxdy=28
Divide the numbers
dxdy=28
Divide the numbers
More Steps
Evaluate
28
Reduce the numbers
14
Calculate
4
dxdy=4
Take the derivative of both sides
dxd(dxdy)=dxd(4)
Calculate the derivative
dx2d2y=dxd(4)
Solution
dx2d2y=0
Show Solution
Graph
