Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the slope
Find the inverse
Evaluate the derivative
Load more
m=−323
Evaluate
y=31x−8x
Simplify
More Steps
Evaluate
31x−8x
Collect like terms by calculating the sum or difference of their coefficients
(31−8)x
Subtract the numbers
More Steps
Evaluate
31−8
Reduce fractions to a common denominator
31−38×3
Write all numerators above the common denominator
31−8×3
Multiply the numbers
31−24
Subtract the numbers
3−23
Use b−a=−ba=−ba to rewrite the fraction
−323
−323x
y=−323x
Solution
m=−323
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
y=31x−8x
Simplify the expression
y=−323x
To test if the graph of y=−323x is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−323(−x)
Multiplying or dividing an even number of negative terms equals a positive
−y=323x
Change the signs both sides
y=−323x
Solution
Symmetry with respect to the origin
Show Solution
Solve the equation
Solve for x
Solve for y
x=−233y
Evaluate
y=31x−8x
Simplify
More Steps
Evaluate
31x−8x
Collect like terms by calculating the sum or difference of their coefficients
(31−8)x
Subtract the numbers
More Steps
Evaluate
31−8
Reduce fractions to a common denominator
31−38×3
Write all numerators above the common denominator
31−8×3
Multiply the numbers
31−24
Subtract the numbers
3−23
Use b−a=−ba=−ba to rewrite the fraction
−323
−323x
y=−323x
Swap the sides of the equation
−323x=y
Change the signs on both sides of the equation
323x=−y
Multiply by the reciprocal
323x×233=−y×233
Multiply
x=−y×233
Solution
x=−233y
Show Solution
Rewrite the equation
r=0θ=arccot(−233)+kπ,k∈Z
Evaluate
y=31x−8x
Simplify
More Steps
Evaluate
31x−8x
Collect like terms by calculating the sum or difference of their coefficients
(31−8)x
Subtract the numbers
More Steps
Evaluate
31−8
Reduce fractions to a common denominator
31−38×3
Write all numerators above the common denominator
31−8×3
Multiply the numbers
31−24
Subtract the numbers
3−23
Use b−a=−ba=−ba to rewrite the fraction
−323
−323x
y=−323x
Multiply both sides of the equation by LCD
y×3=−323x×3
Use the commutative property to reorder the terms
3y=−323x×3
Simplify the equation
3y=−23x
Move the expression to the left side
3y+23x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
3sin(θ)×r+23cos(θ)×r=0
Factor the expression
(3sin(θ)+23cos(θ))r=0
Separate into possible cases
r=03sin(θ)+23cos(θ)=0
Solution
More Steps
Evaluate
3sin(θ)+23cos(θ)=0
Move the expression to the right side
23cos(θ)=0−3sin(θ)
Subtract the terms
23cos(θ)=−3sin(θ)
Divide both sides
sin(θ)23cos(θ)=−3
Divide the terms
More Steps
Evaluate
sin(θ)23cos(θ)
Rewrite the expression
23sin−1(θ)cos(θ)
Rewrite the expression
23cot(θ)
23cot(θ)=−3
Multiply both sides of the equation by 231
23cot(θ)×231=−3×231
Calculate
cot(θ)=−3×231
Multiply the numbers
cot(θ)=−233
Use the inverse trigonometric function
θ=arccot(−233)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(−233)+kπ,k∈Z
r=0θ=arccot(−233)+kπ,k∈Z
Show Solution
Graph
