Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
4x−7y×10=0
To find the x-intercept,set y=0
4x−7×0×10=0
Any expression multiplied by 0 equals 0
4x−0=0
Removing 0 doesn't change the value,so remove it from the expression
4x=0
Solution
x=0
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Solve the equation
Solve for x
Solve for y
x=235y
Evaluate
4x−7y×10=0
Multiply the terms
4x−70y=0
Move the expression to the right-hand side and change its sign
4x=0+70y
Add the terms
4x=70y
Divide both sides
44x=470y
Divide the numbers
x=470y
Solution
x=235y
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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
4x−7y10=0
Simplify the expression
4x−70y=0
To test if the graph of 4x−70y=0 is symmetry with respect to the origin,substitute -x for x and -y for y
4(−x)−70(−y)=0
Evaluate
More Steps

Evaluate
4(−x)−70(−y)
Multiply the numbers
−4x−70(−y)
Multiply the numbers
−4x−(−70y)
Rewrite the expression
−4x+70y
−4x+70y=0
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=arctan(352)+kπ,k∈Z
Evaluate
4x−7y×10=0
Evaluate
4x−70y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4cos(θ)×r−70sin(θ)×r=0
Factor the expression
(4cos(θ)−70sin(θ))r=0
Separate into possible cases
r=04cos(θ)−70sin(θ)=0
Solution
More Steps

Evaluate
4cos(θ)−70sin(θ)=0
Move the expression to the right side
−70sin(θ)=0−4cos(θ)
Subtract the terms
−70sin(θ)=−4cos(θ)
Divide both sides
cos(θ)−70sin(θ)=−4
Divide the terms
More Steps

Evaluate
cos(θ)−70sin(θ)
Use b−a=−ba=−ba to rewrite the fraction
−cos(θ)70sin(θ)
Rewrite the expression
−70cos−1(θ)sin(θ)
Rewrite the expression
−70tan(θ)
−70tan(θ)=−4
Multiply both sides of the equation by −701
−70tan(θ)(−701)=−4(−701)
Calculate
tan(θ)=−4(−701)
Calculate
More Steps

Evaluate
−4(−701)
Multiplying or dividing an even number of negative terms equals a positive
4×701
Reduce the numbers
2×351
Multiply the numbers
352
tan(θ)=352
Use the inverse trigonometric function
θ=arctan(352)
Add the period of kπ,k∈Z to find all solutions
θ=arctan(352)+kπ,k∈Z
r=0θ=arctan(352)+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=352
Calculate
4x−7y10=0
Simplify the expression
4x−70y=0
Take the derivative of both sides
dxd(4x−70y)=dxd(0)
Calculate the derivative
More Steps

Evaluate
dxd(4x−70y)
Use differentiation rules
dxd(4x)+dxd(−70y)
Evaluate the derivative
More Steps

Evaluate
dxd(4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x)
Use dxdxn=nxn−1 to find derivative
4×1
Any expression multiplied by 1 remains the same
4
4+dxd(−70y)
Evaluate the derivative
More Steps

Evaluate
dxd(−70y)
Use differentiation rules
dyd(−70y)×dxdy
Evaluate the derivative
−70dxdy
4−70dxdy
4−70dxdy=dxd(0)
Calculate the derivative
4−70dxdy=0
Move the constant to the right-hand side and change its sign
−70dxdy=0−4
Removing 0 doesn't change the value,so remove it from the expression
−70dxdy=−4
Change the signs on both sides of the equation
70dxdy=4
Divide both sides
7070dxdy=704
Divide the numbers
dxdy=704
Solution
dxdy=352
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
4x−7y10=0
Simplify the expression
4x−70y=0
Take the derivative of both sides
dxd(4x−70y)=dxd(0)
Calculate the derivative
More Steps

Evaluate
dxd(4x−70y)
Use differentiation rules
dxd(4x)+dxd(−70y)
Evaluate the derivative
More Steps

Evaluate
dxd(4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
4×dxd(x)
Use dxdxn=nxn−1 to find derivative
4×1
Any expression multiplied by 1 remains the same
4
4+dxd(−70y)
Evaluate the derivative
More Steps

Evaluate
dxd(−70y)
Use differentiation rules
dyd(−70y)×dxdy
Evaluate the derivative
−70dxdy
4−70dxdy
4−70dxdy=dxd(0)
Calculate the derivative
4−70dxdy=0
Move the constant to the right-hand side and change its sign
−70dxdy=0−4
Removing 0 doesn't change the value,so remove it from the expression
−70dxdy=−4
Change the signs on both sides of the equation
70dxdy=4
Divide both sides
7070dxdy=704
Divide the numbers
dxdy=704
Cancel out the common factor 2
dxdy=352
Take the derivative of both sides
dxd(dxdy)=dxd(352)
Calculate the derivative
dx2d2y=dxd(352)
Solution
dx2d2y=0
Show Solution
