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Question
2x-3y=6
Function
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\text{Find the }x\text{-intercept/zero}
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Find the y-intercept
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Find the slope
x=3
Evaluate
2x-3y=6
\text{To find the }x\text{-intercept,set }y\text{=0}
2x-3\times 0=6
Any expression multiplied by 0 equals 0
2x-0=6
Removing 0 doesn't change the value,so remove it from the expression
2x=6
Divide both sides
\frac{2x}{2}=\frac{6}{2}
Divide the numbers
x=\frac{6}{2}
Solution
More Steps
Evaluate
\frac{6}{2}
Reduce the numbers
\frac{3}{1}
Calculate
3
x=3
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=\frac{6+3y}{2}
Evaluate
2x-3y=6
Move the expression to the right-hand side and change its sign
2x=6+3y
Divide both sides
\frac{2x}{2}=\frac{6+3y}{2}
Solution
x=\frac{6+3y}{2}
Show Solutions
Testing for symmetry
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Testing for symmetry about the origin
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Testing for symmetry about the x-axis
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Testing for symmetry about the y-axis
\textrm{Not symmetry with respect to the origin}
Evaluate
2x-3y=6
\text{To test if the graph of }2x-3y=6\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
2\left(-x\right)-3\left(-y\right)=6
Evaluate
More Steps
Evaluate
2\left(-x\right)-3\left(-y\right)
Multiply the numbers
-2x-3\left(-y\right)
Multiply the numbers
-2x-\left(-3y\right)
Rewrite the expression
-2x+3y
-2x+3y=6
Solution
\textrm{Not symmetry with respect to the origin}
Show Solutions
Rewrite the equation
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Rewrite in polar form
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Rewrite in slope-intercept form
r=\frac{6}{2\cos\left(\theta \right)-3\sin\left(\theta \right)}
Evaluate
2x-3y=6
\text{To convert the equation to polar coordinates,substitute }r\cos\left(\theta \right)\text{ for }x\text{ and }r\sin\left(\theta \right)\text{ for }y
2\cos\left(\theta \right)\times r-3\sin\left(\theta \right)\times r=6
Factor the expression
\left(2\cos\left(\theta \right)-3\sin\left(\theta \right)\right)r=6
Solution
r=\frac{6}{2\cos\left(\theta \right)-3\sin\left(\theta \right)}
Show Solutions
Find the first derivative
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\text{Find the derivative with respect to }x
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\text{Find the derivative with respect to }y
\frac{dy}{dx}=\frac{2}{3}
Calculate
2x-3y=6
Take the derivative of both sides
\frac{d}{dx}\left(2x-3y\right)=\frac{d}{dx}\left(6\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(2x-3y\right)
Use differentiation rules
\frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(-3y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(2x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
2\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
2\times 1
Any expression multiplied by 1 remains the same
2
2+\frac{d}{dx}\left(-3y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-3y\right)
Use differentiation rules
\frac{d}{dy}\left(-3y\right)\times \frac{dy}{dx}
Evaluate the derivative
-3\frac{dy}{dx}
2-3\frac{dy}{dx}
2-3\frac{dy}{dx}=\frac{d}{dx}\left(6\right)
Calculate the derivative
2-3\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-3\frac{dy}{dx}=0-2
Removing 0 doesn't change the value,so remove it from the expression
-3\frac{dy}{dx}=-2
Change the signs on both sides of the equation
3\frac{dy}{dx}=2
Divide both sides
\frac{3\frac{dy}{dx}}{3}=\frac{2}{3}
Solution
\frac{dy}{dx}=\frac{2}{3}
Show Solutions
Find the second derivative
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\text{Find the second derivative with respect to }x
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\text{Find the second derivative with respect to }y
\frac{d^2y}{dx^2}=0
Calculate
2x-3y=6
Take the derivative of both sides
\frac{d}{dx}\left(2x-3y\right)=\frac{d}{dx}\left(6\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(2x-3y\right)
Use differentiation rules
\frac{d}{dx}\left(2x\right)+\frac{d}{dx}\left(-3y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(2x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
2\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
2\times 1
Any expression multiplied by 1 remains the same
2
2+\frac{d}{dx}\left(-3y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-3y\right)
Use differentiation rules
\frac{d}{dy}\left(-3y\right)\times \frac{dy}{dx}
Evaluate the derivative
-3\frac{dy}{dx}
2-3\frac{dy}{dx}
2-3\frac{dy}{dx}=\frac{d}{dx}\left(6\right)
Calculate the derivative
2-3\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-3\frac{dy}{dx}=0-2
Removing 0 doesn't change the value,so remove it from the expression
-3\frac{dy}{dx}=-2
Change the signs on both sides of the equation
3\frac{dy}{dx}=2
Divide both sides
\frac{3\frac{dy}{dx}}{3}=\frac{2}{3}
Divide the numbers
\frac{dy}{dx}=\frac{2}{3}
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(\frac{2}{3}\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{2}{3}\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
