Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
x×10=5y
To find the x-intercept,set y=0
x×10=5×0
Any expression multiplied by 0 equals 0
x×10=0
Use the commutative property to reorder the terms
10x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=2y
Evaluate
x×10=5y
Use the commutative property to reorder the terms
10x=5y
Divide both sides
1010x=105y
Divide the numbers
x=105y
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
x10=5y
Simplify the expression
10x=5y
To test if the graph of 10x=5y is symmetry with respect to the origin,substitute -x for x and -y for y
10(−x)=5(−y)
Evaluate
−10x=5(−y)
Evaluate
−10x=−5y
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(2)+kπ,k∈Z
Evaluate
x×10=5y
Use the commutative property to reorder the terms
10x=5y
Move the expression to the left side
10x−5y=0
To convert the equation to polar coordinates,substitute rcos(θ) for x and rsin(θ) for y
10cos(θ)×r−5sin(θ)×r=0
Factor the expression
(10cos(θ)−5sin(θ))r=0
Separate into possible cases
r=010cos(θ)−5sin(θ)=0
Solution
More Steps
Evaluate
10cos(θ)−5sin(θ)=0
Move the expression to the right side
−5sin(θ)=0−10cos(θ)
Subtract the terms
−5sin(θ)=−10cos(θ)
Divide both sides
cos(θ)−5sin(θ)=−10
Divide the terms
More Steps
Evaluate
cos(θ)−5sin(θ)
Use b−a=−ba=−ba to rewrite the fraction
−cos(θ)5sin(θ)
Rewrite the expression
−5cos−1(θ)sin(θ)
Rewrite the expression
−5tan(θ)
−5tan(θ)=−10
Multiply both sides of the equation by −51
−5tan(θ)(−51)=−10(−51)
Calculate
tan(θ)=−10(−51)
Calculate
More Steps
Evaluate
−10(−51)
Multiplying or dividing an even number of negative terms equals a positive
10×51
Reduce the numbers
2×1
Simplify
2
tan(θ)=2
Use the inverse trigonometric function
θ=arctan(2)
Add the period of kπ,k∈Z to find all solutions
θ=arctan(2)+kπ,k∈Z
r=0θ=arctan(2)+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
x10=5y
Simplify the expression
10x=5y
Take the derivative of both sides
dxd(10x)=dxd(5y)
Calculate the derivative
More Steps
Evaluate
dxd(10x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
10×dxd(x)
Use dxdxn=nxn−1 to find derivative
10×1
Any expression multiplied by 1 remains the same
10
10=dxd(5y)
Calculate the derivative
More Steps
Evaluate
dxd(5y)
Use differentiation rules
dyd(5y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(5y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dyd(y)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5dxdy
10=5dxdy
Swap the sides of the equation
5dxdy=10
Divide both sides
55dxdy=510
Divide the numbers
dxdy=510
Solution
More Steps
Evaluate
510
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
x10=5y
Simplify the expression
10x=5y
Take the derivative of both sides
dxd(10x)=dxd(5y)
Calculate the derivative
More Steps
Evaluate
dxd(10x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
10×dxd(x)
Use dxdxn=nxn−1 to find derivative
10×1
Any expression multiplied by 1 remains the same
10
10=dxd(5y)
Calculate the derivative
More Steps
Evaluate
dxd(5y)
Use differentiation rules
dyd(5y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(5y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dyd(y)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5dxdy
10=5dxdy
Swap the sides of the equation
5dxdy=10
Divide both sides
55dxdy=510
Divide the numbers
dxdy=510
Divide the numbers
More Steps
Evaluate
510
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