Algebra
Calculus
Trigonometry
Matrix
Question
y×12=−2x
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
y×12=−2x
To find the x-intercept,set y=0
0×12=−2x
Any expression multiplied by 0 equals 0
0=−2x
Swap the sides of the equation
−2x=0
Change the signs on both sides of the equation
2x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=−6y
Evaluate
y×12=−2x
Use the commutative property to reorder the terms
12y=−2x
Swap the sides of the equation
−2x=12y
Change the signs on both sides of the equation
2x=−12y
Divide both sides
22x=2−12y
Divide the numbers
x=2−12y
Solution
More Steps
Evaluate
2−12y
Reduce the numbers
1−6y
Calculate
−6y
x=−6y
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
y12=−2x
Simplify the expression
12y=−2x
To test if the graph of 12y=−2x is symmetry with respect to the origin,substitute -x for x and -y for y
12(−y)=−2(−x)
Evaluate
−12y=−2(−x)
Evaluate
−12y=2x
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(−6)+kπ,k∈Z
Evaluate
y×12=−2x
Use the commutative property to reorder the terms
12y=−2x
Move the expression to the left side
12y+2x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
12sin(θ)×r+2cos(θ)×r=0
Factor the expression
(12sin(θ)+2cos(θ))r=0
Separate into possible cases
r=012sin(θ)+2cos(θ)=0
Solution
More Steps
Evaluate
12sin(θ)+2cos(θ)=0
Move the expression to the right side
2cos(θ)=0−12sin(θ)
Subtract the terms
2cos(θ)=−12sin(θ)
Divide both sides
sin(θ)2cos(θ)=−12
Divide the terms
More Steps
Evaluate
sin(θ)2cos(θ)
Rewrite the expression
2sin−1(θ)cos(θ)
Rewrite the expression
2cot(θ)
2cot(θ)=−12
Multiply both sides of the equation by 21
2cot(θ)×21=−12×21
Calculate
cot(θ)=−12×21
Calculate
More Steps
Evaluate
−12×21
Reduce the numbers
−6×1
Simplify
−6
cot(θ)=−6
Use the inverse trigonometric function
θ=arccot(−6)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(−6)+kπ,k∈Z
r=0θ=arccot(−6)+kπ,k∈Z
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−61
Calculate
y12=−2x
Simplify the expression
12y=−2x
Take the derivative of both sides
dxd(12y)=dxd(−2x)
Calculate the derivative
More Steps
Evaluate
dxd(12y)
Use differentiation rules
dyd(12y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(12y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
12×dyd(y)
Use dxdxn=nxn−1 to find derivative
12×1
Any expression multiplied by 1 remains the same
12
12dxdy
12dxdy=dxd(−2x)
Calculate the derivative
More Steps
Evaluate
dxd(−2x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−2×dxd(x)
Use dxdxn=nxn−1 to find derivative
−2×1
Any expression multiplied by 1 remains the same
−2
12dxdy=−2
Divide both sides
1212dxdy=12−2
Divide the numbers
dxdy=12−2
Solution
More Steps
Evaluate
12−2
Cancel out the common factor 2
6−1
Use b−a=−ba=−ba to rewrite the fraction
−61
dxdy=−61
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
y12=−2x
Simplify the expression
12y=−2x
Take the derivative of both sides
dxd(12y)=dxd(−2x)
Calculate the derivative
More Steps
Evaluate
dxd(12y)
Use differentiation rules
dyd(12y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(12y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
12×dyd(y)
Use dxdxn=nxn−1 to find derivative
12×1
Any expression multiplied by 1 remains the same
12
12dxdy
12dxdy=dxd(−2x)
Calculate the derivative
More Steps
Evaluate
dxd(−2x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−2×dxd(x)
Use dxdxn=nxn−1 to find derivative
−2×1
Any expression multiplied by 1 remains the same
−2
12dxdy=−2
Divide both sides
1212dxdy=12−2
Divide the numbers
dxdy=12−2
Divide the numbers
More Steps
Evaluate
12−2
Cancel out the common factor 2
6−1
Use b−a=−ba=−ba to rewrite the fraction
−61
dxdy=−61
Take the derivative of both sides
dxd(dxdy)=dxd(−61)
Calculate the derivative
dx2d2y=dxd(−61)
Solution
dx2d2y=0
Show Solution
Graph
