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Question
4x+2y=14
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{7}{2}
Evaluate
4x+2y=14
\text{To find the }x\text{-intercept,set }y\text{=0}
4x+2\times 0=14
Any expression multiplied by 0 equals 0
4x+0=14
Removing 0 doesn't change the value,so remove it from the expression
4x=14
Divide both sides
\frac{4x}{4}=\frac{14}{4}
Divide the numbers
x=\frac{14}{4}
Solution
x=\frac{7}{2}
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=\frac{7-y}{2}
Evaluate
4x+2y=14
Move the expression to the right-hand side and change its sign
4x=14-2y
Divide both sides
\frac{4x}{4}=\frac{14-2y}{4}
Divide the numbers
x=\frac{14-2y}{4}
Solution
More Steps
Evaluate
\frac{14-2y}{4}
Rewrite the expression
\frac{2\left(7-y\right)}{4}
\text{Cancel out the common factor }2
\frac{7-y}{2}
x=\frac{7-y}{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
4x+2y=14
\text{To test if the graph of }4x+2y=14\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
4\left(-x\right)+2\left(-y\right)=14
Evaluate
More Steps
Evaluate
4\left(-x\right)+2\left(-y\right)
Multiply the numbers
-4x+2\left(-y\right)
Multiply the numbers
-4x-2y
-4x-2y=14
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 standard form
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Rewrite in slope-intercept form
r=\frac{7}{2\cos\left(\theta \right)+\sin\left(\theta \right)}
Evaluate
4x+2y=14
\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
4\cos\left(\theta \right)\times r+2\sin\left(\theta \right)\times r=14
Factor the expression
\left(4\cos\left(\theta \right)+2\sin\left(\theta \right)\right)r=14
Solution
r=\frac{7}{2\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}=-2
Calculate
4x+2y=14
Take the derivative of both sides
\frac{d}{dx}\left(4x+2y\right)=\frac{d}{dx}\left(14\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(4x+2y\right)
Use differentiation rules
\frac{d}{dx}\left(4x\right)+\frac{d}{dx}\left(2y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(4x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
4\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
4\times 1
Any expression multiplied by 1 remains the same
4
4+\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}
4+2\frac{dy}{dx}
4+2\frac{dy}{dx}=\frac{d}{dx}\left(14\right)
Calculate the derivative
4+2\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
2\frac{dy}{dx}=0-4
Removing 0 doesn't change the value,so remove it from the expression
2\frac{dy}{dx}=-4
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{-4}{2}
Divide the numbers
\frac{dy}{dx}=\frac{-4}{2}
Solution
More Steps
Evaluate
\frac{-4}{2}
Reduce the numbers
\frac{-2}{1}
Calculate
-2
\frac{dy}{dx}=-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
4x+2y=14
Take the derivative of both sides
\frac{d}{dx}\left(4x+2y\right)=\frac{d}{dx}\left(14\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(4x+2y\right)
Use differentiation rules
\frac{d}{dx}\left(4x\right)+\frac{d}{dx}\left(2y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(4x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
4\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
4\times 1
Any expression multiplied by 1 remains the same
4
4+\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}
4+2\frac{dy}{dx}
4+2\frac{dy}{dx}=\frac{d}{dx}\left(14\right)
Calculate the derivative
4+2\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
2\frac{dy}{dx}=0-4
Removing 0 doesn't change the value,so remove it from the expression
2\frac{dy}{dx}=-4
Divide both sides
\frac{2\frac{dy}{dx}}{2}=\frac{-4}{2}
Divide the numbers
\frac{dy}{dx}=\frac{-4}{2}
Divide the numbers
More Steps
Evaluate
\frac{-4}{2}
Reduce the numbers
\frac{-2}{1}
Calculate
-2
\frac{dy}{dx}=-2
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(-2\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(-2\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
