Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=533
Evaluate
5(x−9)−6(y−2)=0
To find the x-intercept,set y=0
5(x−9)−6(0−2)=0
Simplify
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Evaluate
5(x−9)−6(0−2)
Removing 0 doesn't change the value,so remove it from the expression
5(x−9)−6(−2)
Multiply the numbers
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Evaluate
6(−2)
Multiplying or dividing an odd number of negative terms equals a negative
−6×2
Multiply the numbers
−12
5(x−9)−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
5(x−9)+12
5(x−9)+12=0
Calculate
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Evaluate
5(x−9)+12
Expand the expression
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Calculate
5(x−9)
Apply the distributive property
5x−5×9
Multiply the numbers
5x−45
5x−45+12
Add the numbers
5x−33
5x−33=0
Move the constant to the right-hand side and change its sign
5x=0+33
Removing 0 doesn't change the value,so remove it from the expression
5x=33
Divide both sides
55x=533
Solution
x=533
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Solve the equation
Solve for x
Solve for y
x=533+6y
Evaluate
5(x−9)−6(y−2)=0
Rewrite the expression
5(x−9)−6y+12=0
Calculate the sum or difference
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Evaluate
5(x−9)−6y+12
Expand the expression
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Calculate
5(x−9)
Apply the distributive property
5x−5×9
Multiply the numbers
5x−45
5x−45−6y+12
Add the numbers
5x−33−6y
5x−33−6y=0
Move the expression to the right-hand side and change its sign
5x=0+33+6y
Removing 0 doesn't change the value,so remove it from the expression
5x=33+6y
Divide both sides
55x=533+6y
Solution
x=533+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
Not symmetry with respect to the origin
Evaluate
5(x−9)−6(y−2)=0
To test if the graph of 5(x−9)−6(y−2)=0 is symmetry with respect to the origin,substitute -x for x and -y for y
5(−x−9)−6(−y−2)=0
Solution
Not 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=5cos(θ)−6sin(θ)33
Evaluate
5(x−9)−6(y−2)=0
Evaluate
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Evaluate
5(x−9)−6(y−2)
Expand the expression
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Calculate
5(x−9)
Apply the distributive property
5x−5×9
Multiply the numbers
5x−45
5x−45−6(y−2)
Expand the expression
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Calculate
−6(y−2)
Apply the distributive property
−6y−(−6×2)
Multiply the numbers
−6y−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−6y+12
5x−45−6y+12
Add the numbers
5x−33−6y
5x−33−6y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
5cos(θ)×r−33−6sin(θ)×r=0
Factor the expression
(5cos(θ)−6sin(θ))r−33=0
Subtract the terms
(5cos(θ)−6sin(θ))r−33−(−33)=0−(−33)
Evaluate
(5cos(θ)−6sin(θ))r=33
Solution
r=5cos(θ)−6sin(θ)33
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=65
Calculate
5(x−9)−6(y−2)=0
Simplify the expression
5x−33−6y=0
Take the derivative of both sides
dxd(5x−33−6y)=dxd(0)
Calculate the derivative
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Evaluate
dxd(5x−33−6y)
Use differentiation rules
dxd(5x)+dxd(−33)+dxd(−6y)
Evaluate the derivative
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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
5+dxd(−33)+dxd(−6y)
Use dxd(c)=0 to find derivative
5+0+dxd(−6y)
Evaluate the derivative
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Evaluate
dxd(−6y)
Use differentiation rules
dyd(−6y)×dxdy
Evaluate the derivative
−6dxdy
5+0−6dxdy
Evaluate
5−6dxdy
5−6dxdy=dxd(0)
Calculate the derivative
5−6dxdy=0
Move the constant to the right-hand side and change its sign
−6dxdy=0−5
Removing 0 doesn't change the value,so remove it from the expression
−6dxdy=−5
Change the signs on both sides of the equation
6dxdy=5
Divide both sides
66dxdy=65
Solution
dxdy=65
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
5(x−9)−6(y−2)=0
Simplify the expression
5x−33−6y=0
Take the derivative of both sides
dxd(5x−33−6y)=dxd(0)
Calculate the derivative
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Evaluate
dxd(5x−33−6y)
Use differentiation rules
dxd(5x)+dxd(−33)+dxd(−6y)
Evaluate the derivative
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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
5+dxd(−33)+dxd(−6y)
Use dxd(c)=0 to find derivative
5+0+dxd(−6y)
Evaluate the derivative
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Evaluate
dxd(−6y)
Use differentiation rules
dyd(−6y)×dxdy
Evaluate the derivative
−6dxdy
5+0−6dxdy
Evaluate
5−6dxdy
5−6dxdy=dxd(0)
Calculate the derivative
5−6dxdy=0
Move the constant to the right-hand side and change its sign
−6dxdy=0−5
Removing 0 doesn't change the value,so remove it from the expression
−6dxdy=−5
Change the signs on both sides of the equation
6dxdy=5
Divide both sides
66dxdy=65
Divide the numbers
dxdy=65
Take the derivative of both sides
dxd(dxdy)=dxd(65)
Calculate the derivative
dx2d2y=dxd(65)
Solution
dx2d2y=0
Show Solution
