Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=56
Evaluate
5x−9=−8y−3
To find the x-intercept,set y=0
5x−9=−8×0−3
Any expression multiplied by 0 equals 0
5x−9=0−3
Removing 0 doesn't change the value,so remove it from the expression
5x−9=−3
Move the constant to the right-hand side and change its sign
5x=−3+9
Add the numbers
5x=6
Divide both sides
55x=56
Solution
x=56
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Solve the equation
Solve for x
Solve for y
x=5−8y+6
Evaluate
5x−9=−8y−3
Move the constant to the right-hand side and change its sign
5x=−8y−3+9
Add the numbers
5x=−8y+6
Divide both sides
55x=5−8y+6
Solution
x=5−8y+6
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Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Not symmetry with respect to the origin
Evaluate
5x−9=−8y−3
To test if the graph of 5x−9=−8y−3 is symmetry with respect to the origin,substitute -x for x and -y for y
5(−x)−9=−8(−y)−3
Evaluate
−5x−9=−8(−y)−3
Evaluate
−5x−9=8y−3
Solution
Not symmetry with respect to the origin
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Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=5cos(θ)+8sin(θ)6
Evaluate
5x−9=−8y−3
Move the expression to the left side
5x−9+8y=−3
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
5cos(θ)×r−9+8sin(θ)×r=−3
Factor the expression
(5cos(θ)+8sin(θ))r−9=−3
Subtract the terms
(5cos(θ)+8sin(θ))r−9−(−9)=−3−(−9)
Evaluate
(5cos(θ)+8sin(θ))r=6
Solution
r=5cos(θ)+8sin(θ)6
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−85
Calculate
5x−9=−8y−3
Take the derivative of both sides
dxd(5x−9)=dxd(−8y−3)
Calculate the derivative
More Steps

Evaluate
dxd(5x−9)
Use differentiation rules
dxd(5x)+dxd(−9)
Evaluate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5+dxd(−9)
Use dxd(c)=0 to find derivative
5+0
Evaluate
5
5=dxd(−8y−3)
Calculate the derivative
More Steps

Evaluate
dxd(−8y−3)
Use differentiation rules
dxd(−8y)+dxd(−3)
Evaluate the derivative
More Steps

Evaluate
dxd(−8y)
Use differentiation rules
dyd(−8y)×dxdy
Evaluate the derivative
−8dxdy
−8dxdy+dxd(−3)
Use dxd(c)=0 to find derivative
−8dxdy+0
Evaluate
−8dxdy
5=−8dxdy
Swap the sides of the equation
−8dxdy=5
Change the signs on both sides of the equation
8dxdy=−5
Divide both sides
88dxdy=8−5
Divide the numbers
dxdy=8−5
Solution
dxdy=−85
Show Solution

Find the second derivative
Find the second derivative with respect to x
Find the second derivative with respect to y
dx2d2y=0
Calculate
5x−9=−8y−3
Take the derivative of both sides
dxd(5x−9)=dxd(−8y−3)
Calculate the derivative
More Steps

Evaluate
dxd(5x−9)
Use differentiation rules
dxd(5x)+dxd(−9)
Evaluate the derivative
More Steps

Evaluate
dxd(5x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
5×dxd(x)
Use dxdxn=nxn−1 to find derivative
5×1
Any expression multiplied by 1 remains the same
5
5+dxd(−9)
Use dxd(c)=0 to find derivative
5+0
Evaluate
5
5=dxd(−8y−3)
Calculate the derivative
More Steps

Evaluate
dxd(−8y−3)
Use differentiation rules
dxd(−8y)+dxd(−3)
Evaluate the derivative
More Steps

Evaluate
dxd(−8y)
Use differentiation rules
dyd(−8y)×dxdy
Evaluate the derivative
−8dxdy
−8dxdy+dxd(−3)
Use dxd(c)=0 to find derivative
−8dxdy+0
Evaluate
−8dxdy
5=−8dxdy
Swap the sides of the equation
−8dxdy=5
Change the signs on both sides of the equation
8dxdy=−5
Divide both sides
88dxdy=8−5
Divide the numbers
dxdy=8−5
Use b−a=−ba=−ba to rewrite the fraction
dxdy=−85
Take the derivative of both sides
dxd(dxdy)=dxd(−85)
Calculate the derivative
dx2d2y=dxd(−85)
Solution
dx2d2y=0
Show Solution
