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Question
8x-6y=-24
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=-3
Evaluate
8x-6y=-24
\text{To find the }x\text{-intercept,set }y\text{=0}
8x-6\times 0=-24
Any expression multiplied by 0 equals 0
8x-0=-24
Removing 0 doesn't change the value,so remove it from the expression
8x=-24
Divide both sides
\frac{8x}{8}=\frac{-24}{8}
Divide the numbers
x=\frac{-24}{8}
Solution
More Steps
Evaluate
\frac{-24}{8}
Reduce the numbers
\frac{-3}{1}
Calculate
-3
x=-3
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=\frac{-12+3y}{4}
Evaluate
8x-6y=-24
Move the expression to the right-hand side and change its sign
8x=-24+6y
Divide both sides
\frac{8x}{8}=\frac{-24+6y}{8}
Divide the numbers
x=\frac{-24+6y}{8}
Solution
More Steps
Evaluate
\frac{-24+6y}{8}
Rewrite the expression
\frac{2\left(-12+3y\right)}{8}
\text{Cancel out the common factor }2
\frac{-12+3y}{4}
x=\frac{-12+3y}{4}
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
8x-6y=-24
\text{To test if the graph of }8x-6y=-24\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
8\left(-x\right)-6\left(-y\right)=-24
Evaluate
More Steps
Evaluate
8\left(-x\right)-6\left(-y\right)
Multiply the numbers
-8x-6\left(-y\right)
Multiply the numbers
-8x-\left(-6y\right)
Rewrite the expression
-8x+6y
-8x+6y=-24
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{12}{4\cos\left(\theta \right)-3\sin\left(\theta \right)}
Evaluate
8x-6y=-24
\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
8\cos\left(\theta \right)\times r-6\sin\left(\theta \right)\times r=-24
Factor the expression
\left(8\cos\left(\theta \right)-6\sin\left(\theta \right)\right)r=-24
Solution
r=-\frac{12}{4\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{4}{3}
Calculate
8x-6y=-24
Take the derivative of both sides
\frac{d}{dx}\left(8x-6y\right)=\frac{d}{dx}\left(-24\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(8x-6y\right)
Use differentiation rules
\frac{d}{dx}\left(8x\right)+\frac{d}{dx}\left(-6y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(8x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
8\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
8\times 1
Any expression multiplied by 1 remains the same
8
8+\frac{d}{dx}\left(-6y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-6y\right)
Use differentiation rules
\frac{d}{dy}\left(-6y\right)\times \frac{dy}{dx}
Evaluate the derivative
-6\frac{dy}{dx}
8-6\frac{dy}{dx}
8-6\frac{dy}{dx}=\frac{d}{dx}\left(-24\right)
Calculate the derivative
8-6\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-6\frac{dy}{dx}=0-8
Removing 0 doesn't change the value,so remove it from the expression
-6\frac{dy}{dx}=-8
Change the signs on both sides of the equation
6\frac{dy}{dx}=8
Divide both sides
\frac{6\frac{dy}{dx}}{6}=\frac{8}{6}
Divide the numbers
\frac{dy}{dx}=\frac{8}{6}
Solution
\frac{dy}{dx}=\frac{4}{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
8x-6y=-24
Take the derivative of both sides
\frac{d}{dx}\left(8x-6y\right)=\frac{d}{dx}\left(-24\right)
Calculate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(8x-6y\right)
Use differentiation rules
\frac{d}{dx}\left(8x\right)+\frac{d}{dx}\left(-6y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(8x\right)
\text{Use differentiation rule }\frac{d}{dx}\left(cf\left(x\right)\right)=c\times\frac{d}{dx}(f(x))
8\times \frac{d}{dx}\left(x\right)
\text{Use }\frac{d}{dx} x^{n}=n x^{n-1}\text{ to find derivative}
8\times 1
Any expression multiplied by 1 remains the same
8
8+\frac{d}{dx}\left(-6y\right)
Evaluate the derivative
More Steps
Evaluate
\frac{d}{dx}\left(-6y\right)
Use differentiation rules
\frac{d}{dy}\left(-6y\right)\times \frac{dy}{dx}
Evaluate the derivative
-6\frac{dy}{dx}
8-6\frac{dy}{dx}
8-6\frac{dy}{dx}=\frac{d}{dx}\left(-24\right)
Calculate the derivative
8-6\frac{dy}{dx}=0
Move the constant to the right-hand side and change its sign
-6\frac{dy}{dx}=0-8
Removing 0 doesn't change the value,so remove it from the expression
-6\frac{dy}{dx}=-8
Change the signs on both sides of the equation
6\frac{dy}{dx}=8
Divide both sides
\frac{6\frac{dy}{dx}}{6}=\frac{8}{6}
Divide the numbers
\frac{dy}{dx}=\frac{8}{6}
\text{Cancel out the common factor }2
\frac{dy}{dx}=\frac{4}{3}
Take the derivative of both sides
\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{d}{dx}\left(\frac{4}{3}\right)
Calculate the derivative
\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{4}{3}\right)
Solution
\frac{d^2y}{dx^2}=0
Show Solutions
Graph
