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Question
x\times 7=2y
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=0
Evaluate
x\times 7=2y
\text{To find the }x\text{-intercept,set }y\text{=0}
x\times 7=2\times 0
Any expression multiplied by 0 equals 0
x\times 7=0
Use the commutative property to reorder the terms
7x=0
Solution
x=0
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=\frac{2y}{7}
Evaluate
x\times 7=2y
Use the commutative property to reorder the terms
7x=2y
Divide both sides
\frac{7x}{7}=\frac{2y}{7}
Solution
x=\frac{2y}{7}
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{Symmetry with respect to the origin}
Evaluate
x7=2y
Simplify the expression
7x=2y
\text{To test if the graph of }7x=2y\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
7\left(-x\right)=2\left(-y\right)
Evaluate
-7x=2\left(-y\right)
Evaluate
-7x=-2y
Solution
\textrm{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 standard form
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Rewrite in slope-intercept form
\begin{align}&r=0\\&\theta =\arctan\left(\frac{7}{2}\right)+k\pi ,k \in \mathbb{Z}\end{align}
Evaluate
x\times 7=2y
Use the commutative property to reorder the terms
7x=2y
Move the expression to the left side
7x-2y=0
\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
7\cos\left(\theta \right)\times r-2\sin\left(\theta \right)\times r=0
Factor the expression
\left(7\cos\left(\theta \right)-2\sin\left(\theta \right)\right)r=0
Separate into possible cases
\begin{align}&r=0\\&7\cos\left(\theta \right)-2\sin\left(\theta \right)=0\end{align}
Solution
More Steps
Evaluate
7\cos\left(\theta \right)-2\sin\left(\theta \right)=0
Move the expression to the right side
-2\sin\left(\theta \right)=0-7\cos\left(\theta \right)
Subtract the terms
-2\sin\left(\theta \right)=-7\cos\left(\theta \right)
Divide both sides
\frac{-2\sin\left(\theta \right)}{\cos\left(\theta \right)}=-7
Divide the terms
More Steps
Evaluate
\frac{-2\sin\left(\theta \right)}{\cos\left(\theta \right)}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
-\frac{2\sin\left(\theta \right)}{\cos\left(\theta \right)}
Rewrite the expression
-2\cos^{-1}\left(\theta \right)\sin\left(\theta \right)
Rewrite the expression
-2\tan\left(\theta \right)
-2\tan\left(\theta \right)=-7
\text{Multiply both sides of the equation by }-\frac{1}{2}
-2\tan\left(\theta \right)\left(-\frac{1}{2}\right)=-7\left(-\frac{1}{2}\right)
Calculate
\tan\left(\theta \right)=-7\left(-\frac{1}{2}\right)
Calculate
More Steps
Evaluate
-7\left(-\frac{1}{2}\right)
Multiplying or dividing an even number of negative terms equals a positive
7\times \frac{1}{2}
Multiply the numbers
\frac{7}{2}
\tan\left(\theta \right)=\frac{7}{2}
Use the inverse trigonometric function
\theta =\arctan\left(\frac{7}{2}\right)
\text{Add the period of }k\pi ,k \in \mathbb{Z}\text{ to find all solutions}
\theta =\arctan\left(\frac{7}{2}\right)+k\pi ,k \in \mathbb{Z}
\begin{align}&r=0\\&\theta =\arctan\left(\frac{7}{2}\right)+k\pi ,k \in \mathbb{Z}\end{align}
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{7}{2}
Calculate
x7=2y
Simplify the expression
7x=2y
Take the derivative of both sides
\frac{d}{dx}\left(7x\right)=\frac{d}{dx}\left(2y\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(7x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
7\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
7\times 1
Any expression multiplied by 1 remains the same
7
7=\frac{d}{dx}\left(2y\right)
Calculate 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
More Steps
Evaluate
\frac{d}{dy}\left(2y\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}{dy}\left(y\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{dy}{dx}
7=2\frac{dy}{dx}
Swap the sides of the equation
2\frac{dy}{dx}=7
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{7}{2}
Solution
\frac{dy}{dx}=\frac{7}{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
x7=2y
Simplify the expression
7x=2y
Take the derivative of both sides
\frac{d}{dx}\left(7x\right)=\frac{d}{dx}\left(2y\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(7x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
7\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
7\times 1
Any expression multiplied by 1 remains the same
7
7=\frac{d}{dx}\left(2y\right)
Calculate 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
More Steps
Evaluate
\frac{d}{dy}\left(2y\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}{dy}\left(y\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{dy}{dx}
7=2\frac{dy}{dx}
Swap the sides of the equation
2\frac{dy}{dx}=7
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{7}{2}
Divide the numbers
\frac{dy}{dx}=\frac{7}{2}
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(\frac{7}{2}\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{7}{2}\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
