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Question
5x-y=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=\frac{6}{5}
Evaluate
5x-y=6
\text{To find the }x\text{-intercept,set }y\text{=0}
5x-0=6
Removing 0 doesn't change the value,so remove it from the expression
5x=6
Divide both sides
\frac{5x}{5}=\frac{6}{5}
Solution
x=\frac{6}{5}
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=\frac{6+y}{5}
Evaluate
5x-y=6
Move the expression to the right-hand side and change its sign
5x=6+y
Divide both sides
\frac{5x}{5}=\frac{6+y}{5}
Solution
x=\frac{6+y}{5}
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
5x-y=6
\text{To test if the graph of }5x-y=6\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
5\left(-x\right)-\left(-y\right)=6
Evaluate
More Steps
Evaluate
5\left(-x\right)-\left(-y\right)
Multiply the numbers
-5x-\left(-y\right)
Rewrite the expression
-5x+y
-5x+y=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}{5\cos\left(\theta \right)-\sin\left(\theta \right)}
Evaluate
5x-y=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
5\cos\left(\theta \right)\times r-\sin\left(\theta \right)\times r=6
Factor the expression
\left(5\cos\left(\theta \right)-\sin\left(\theta \right)\right)r=6
Solution
r=\frac{6}{5\cos\left(\theta \right)-\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}=5
Calculate
5x-y=6
Take the derivative of both sides
\frac{d}{dx}\left(5x-y\right)=\frac{d}{dx}\left(6\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(5x-y\right)
Use differentiation rules
\frac{d}{dx}\left(5x\right)+\frac{d}{dx}\left(-y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(5x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
5\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
5\times 1
Any expression multiplied by 1 remains the same
5
5+\frac{d}{dx}\left(-y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-y\right)
Use differentiation rules
\frac{d}{dy}\left(-y\right)\times \frac{dy}{dx}
Evaluate the derivative
-\frac{dy}{dx}
5-\frac{dy}{dx}
5-\frac{dy}{dx}=\frac{d}{dx}\left(6\right)
Calculate the derivative
5-\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-\frac{dy}{dx}=0-5
Removing 0 doesn't change the value,so remove it from the expression
-\frac{dy}{dx}=-5
Solution
\frac{dy}{dx}=5
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
5x-y=6
Take the derivative of both sides
\frac{d}{dx}\left(5x-y\right)=\frac{d}{dx}\left(6\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(5x-y\right)
Use differentiation rules
\frac{d}{dx}\left(5x\right)+\frac{d}{dx}\left(-y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(5x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
5\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
5\times 1
Any expression multiplied by 1 remains the same
5
5+\frac{d}{dx}\left(-y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-y\right)
Use differentiation rules
\frac{d}{dy}\left(-y\right)\times \frac{dy}{dx}
Evaluate the derivative
-\frac{dy}{dx}
5-\frac{dy}{dx}
5-\frac{dy}{dx}=\frac{d}{dx}\left(6\right)
Calculate the derivative
5-\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-\frac{dy}{dx}=0-5
Removing 0 doesn't change the value,so remove it from the expression
-\frac{dy}{dx}=-5
Change the signs on both sides of the equation
\frac{dy}{dx}=5
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(5\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(5\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
