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Question
x+3y=2
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=2
Evaluate
x+3y=2
\text{To find the }x\text{-intercept,set }y\text{=0}
x+3\times 0=2
Any expression multiplied by 0 equals 0
x+0=2
Solution
x=2
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Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=2-3y
Evaluate
x+3y=2
Solution
x=2-3y
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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
x+3y=2
\text{To test if the graph of }x+3y=2\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
-x+3\left(-y\right)=2
Evaluate
-x-3y=2
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{2}{\cos\left(\theta \right)+3\sin\left(\theta \right)}
Evaluate
x+3y=2
\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
\cos\left(\theta \right)\times r+3\sin\left(\theta \right)\times r=2
Factor the expression
\left(\cos\left(\theta \right)+3\sin\left(\theta \right)\right)r=2
Solution
r=\frac{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{1}{3}
Calculate
x+3y=2
Take the derivative of both sides
\frac{d}{dx}\left(x+3y\right)=\frac{d}{dx}\left(2\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(x+3y\right)
Use differentiation rules
\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(3y\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
1+\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}
1+3\frac{dy}{dx}
1+3\frac{dy}{dx}=\frac{d}{dx}\left(2\right)
Calculate the derivative
1+3\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
3\frac{dy}{dx}=0-1
Removing 0 doesn't change the value,so remove it from the expression
3\frac{dy}{dx}=-1
Divide both sides
\frac{3\frac{dy}{dx}}{3}=\frac{-1}{3}
Divide the numbers
\frac{dy}{dx}=\frac{-1}{3}
Solution
\frac{dy}{dx}=-\frac{1}{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
x+3y=2
Take the derivative of both sides
\frac{d}{dx}\left(x+3y\right)=\frac{d}{dx}\left(2\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(x+3y\right)
Use differentiation rules
\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(3y\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
1+\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}
1+3\frac{dy}{dx}
1+3\frac{dy}{dx}=\frac{d}{dx}\left(2\right)
Calculate the derivative
1+3\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
3\frac{dy}{dx}=0-1
Removing 0 doesn't change the value,so remove it from the expression
3\frac{dy}{dx}=-1
Divide both sides
\frac{3\frac{dy}{dx}}{3}=\frac{-1}{3}
Divide the numbers
\frac{dy}{dx}=\frac{-1}{3}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
\frac{dy}{dx}=-\frac{1}{3}
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(-\frac{1}{3}\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(-\frac{1}{3}\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
