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Question
x-2y=4
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=4
Evaluate
x-2y=4
\text{To find the }x\text{-intercept,set }y\text{=0}
x-2\times 0=4
Any expression multiplied by 0 equals 0
x-0=4
Solution
x=4
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Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=4+2y
Evaluate
x-2y=4
Solution
x=4+2y
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
x-2y=4
\text{To test if the graph of }x-2y=4\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
-x-2\left(-y\right)=4
Evaluate
More Steps
Evaluate
-x-2\left(-y\right)
Multiply the numbers
-x-\left(-2y\right)
Rewrite the expression
-x+2y
-x+2y=4
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{4}{\cos\left(\theta \right)-2\sin\left(\theta \right)}
Evaluate
x-2y=4
\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-2\sin\left(\theta \right)\times r=4
Factor the expression
\left(\cos\left(\theta \right)-2\sin\left(\theta \right)\right)r=4
Solution
r=\frac{4}{\cos\left(\theta \right)-2\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}{2}
Calculate
x-2y=4
Take the derivative of both sides
\frac{d}{dx}\left(x-2y\right)=\frac{d}{dx}\left(4\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(x-2y\right)
Use differentiation rules
\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2y\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
1+\frac{d}{dx}\left(-2y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-2y\right)
Use differentiation rules
\frac{d}{dy}\left(-2y\right)\times \frac{dy}{dx}
Evaluate the derivative
-2\frac{dy}{dx}
1-2\frac{dy}{dx}
1-2\frac{dy}{dx}=\frac{d}{dx}\left(4\right)
Calculate the derivative
1-2\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-2\frac{dy}{dx}=0-1
Removing 0 doesn't change the value,so remove it from the expression
-2\frac{dy}{dx}=-1
Change the signs on both sides of the equation
2\frac{dy}{dx}=1
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{1}{2}
Solution
\frac{dy}{dx}=\frac{1}{2}
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-2y=4
Take the derivative of both sides
\frac{d}{dx}\left(x-2y\right)=\frac{d}{dx}\left(4\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(x-2y\right)
Use differentiation rules
\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(-2y\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
1+\frac{d}{dx}\left(-2y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-2y\right)
Use differentiation rules
\frac{d}{dy}\left(-2y\right)\times \frac{dy}{dx}
Evaluate the derivative
-2\frac{dy}{dx}
1-2\frac{dy}{dx}
1-2\frac{dy}{dx}=\frac{d}{dx}\left(4\right)
Calculate the derivative
1-2\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-2\frac{dy}{dx}=0-1
Removing 0 doesn't change the value,so remove it from the expression
-2\frac{dy}{dx}=-1
Change the signs on both sides of the equation
2\frac{dy}{dx}=1
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{1}{2}
Divide the numbers
\frac{dy}{dx}=\frac{1}{2}
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(\frac{1}{2}\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{1}{2}\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
