Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
5y×15=5x
To find the x-intercept,set y=0
5×0×15=5x
Any expression multiplied by 0 equals 0
0=5x
Swap the sides of the equation
5x=0
Solution
x=0
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Solve the equation
Solve for x
Solve for y
x=15y
Evaluate
5y×15=5x
Multiply the terms
75y=5x
Swap the sides of the equation
5x=75y
Divide both sides
55x=575y
Divide the numbers
x=575y
Solution
More Steps

Evaluate
575y
Reduce the numbers
115y
Calculate
15y
x=15y
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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
5y15=5x
Simplify the expression
75y=5x
To test if the graph of 75y=5x is symmetry with respect to the origin,substitute -x for x and -y for y
75(−y)=5(−x)
Evaluate
−75y=5(−x)
Evaluate
−75y=−5x
Solution
Symmetry with respect to the origin
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Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=0θ=arccot(15)+kπ,k∈Z
Evaluate
5y×15=5x
Evaluate
75y=5x
Move the expression to the left side
75y−5x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
75sin(θ)×r−5cos(θ)×r=0
Factor the expression
(75sin(θ)−5cos(θ))r=0
Separate into possible cases
r=075sin(θ)−5cos(θ)=0
Solution
More Steps

Evaluate
75sin(θ)−5cos(θ)=0
Move the expression to the right side
−5cos(θ)=0−75sin(θ)
Subtract the terms
−5cos(θ)=−75sin(θ)
Divide both sides
sin(θ)−5cos(θ)=−75
Divide the terms
More Steps

Evaluate
sin(θ)−5cos(θ)
Use b−a=−ba=−ba to rewrite the fraction
−sin(θ)5cos(θ)
Rewrite the expression
−5sin−1(θ)cos(θ)
Rewrite the expression
−5cot(θ)
−5cot(θ)=−75
Multiply both sides of the equation by −51
−5cot(θ)(−51)=−75(−51)
Calculate
cot(θ)=−75(−51)
Calculate
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Evaluate
−75(−51)
Multiplying or dividing an even number of negative terms equals a positive
75×51
Reduce the numbers
15×1
Simplify
15
cot(θ)=15
Use the inverse trigonometric function
θ=arccot(15)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(15)+kπ,k∈Z
r=0θ=arccot(15)+kπ,k∈Z
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=151
Calculate
5y15=5x
Simplify the expression
75y=5x
Take the derivative of both sides
dxd(75y)=dxd(5x)
Calculate the derivative
More Steps

Evaluate
dxd(75y)
Use differentiation rules
dyd(75y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(75y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
75×dyd(y)
Use dxdxn=nxn−1 to find derivative
75×1
Any expression multiplied by 1 remains the same
75
75dxdy
75dxdy=dxd(5x)
Calculate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
75dxdy=5
Divide both sides
7575dxdy=755
Divide the numbers
dxdy=755
Solution
dxdy=151
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
5y15=5x
Simplify the expression
75y=5x
Take the derivative of both sides
dxd(75y)=dxd(5x)
Calculate the derivative
More Steps

Evaluate
dxd(75y)
Use differentiation rules
dyd(75y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(75y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
75×dyd(y)
Use dxdxn=nxn−1 to find derivative
75×1
Any expression multiplied by 1 remains the same
75
75dxdy
75dxdy=dxd(5x)
Calculate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
75dxdy=5
Divide both sides
7575dxdy=755
Divide the numbers
dxdy=755
Cancel out the common factor 5
dxdy=151
Take the derivative of both sides
dxd(dxdy)=dxd(151)
Calculate the derivative
dx2d2y=dxd(151)
Solution
dx2d2y=0
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