Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=223
Evaluate
y−5=−32(x−4)
To find the x-intercept,set y=0
0−5=−32(x−4)
Removing 0 doesn't change the value,so remove it from the expression
−5=−32(x−4)
Simplify
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Evaluate
−32(x−4)
Multiply the terms
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Evaluate
32(x−4)
Apply the distributive property
32x−32×4
Multiply the numbers
32x−38
−(32x−38)
Calculate
−32x+38
−5=−32x+38
Swap the sides of the equation
−32x+38=−5
Move the constant to the right-hand side and change its sign
−32x=−5−38
Subtract the numbers
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Evaluate
−5−38
Reduce fractions to a common denominator
−35×3−38
Write all numerators above the common denominator
3−5×3−8
Multiply the numbers
3−15−8
Subtract the numbers
3−23
Use b−a=−ba=−ba to rewrite the fraction
−323
−32x=−323
Change the signs on both sides of the equation
32x=323
Multiply by the reciprocal
32x×23=323×23
Multiply
x=323×23
Solution
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Evaluate
323×23
Reduce the numbers
23×21
Multiply the numbers
223
x=223
Show Solution

Solve the equation
Solve for x
Solve for y
x=2−3y+23
Evaluate
y−5=−32(x−4)
Simplify
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Evaluate
−32(x−4)
Multiply the terms
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Evaluate
32(x−4)
Apply the distributive property
32x−32×4
Multiply the numbers
32x−38
−(32x−38)
Calculate
−32x+38
y−5=−32x+38
Swap the sides of the equation
−32x+38=y−5
Move the constant to the right-hand side and change its sign
−32x=y−5−38
Subtract the terms
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Evaluate
y−5−38
Reduce fractions to a common denominator
3y×3−35×3−38
Write all numerators above the common denominator
3y×3−5×3−8
Use the commutative property to reorder the terms
33y−5×3−8
Multiply the numbers
33y−15−8
Subtract the numbers
33y−23
−32x=33y−23
Change the signs on both sides of the equation
32x=3−3y+23
Multiply by the reciprocal
32x×23=3−3y+23×23
Multiply
x=3−3y+23×23
Solution
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Evaluate
3−3y+23×23
Rewrite the expression
−33y−23×23
Reduce the numbers
−(3y−23)×21
Calculate the product
2−3y+23
x=2−3y+23
Show Solution

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
y−5=−32(x−4)
Simplify the expression
y−5=−32x+38
To test if the graph of y−5=−32x+38 is symmetry with respect to the origin,substitute -x for x and -y for y
−y−5=−32(−x)+38
Multiplying or dividing an even number of negative terms equals a positive
−y−5=32x+38
Solution
Not symmetry with respect to the origin
Show Solution

Rewrite the equation
Rewrite in polar form
Rewrite in standard form
Rewrite in slope-intercept form
r=3sin(θ)+2cos(θ)23
Evaluate
y−5=−32(x−4)
Evaluate
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Evaluate
−32(x−4)
Multiply the terms
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Evaluate
32(x−4)
Apply the distributive property
32x−32×4
Multiply the numbers
32x−38
−(32x−38)
Calculate
−32x+38
y−5=−32x+38
Multiply both sides of the equation by LCD
(y−5)×3=(−32x+38)×3
Simplify the equation
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Evaluate
(y−5)×3
Apply the distributive property
y×3−5×3
Use the commutative property to reorder the terms
3y−5×3
Multiply the numbers
3y−15
3y−15=(−32x+38)×3
Simplify the equation
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Evaluate
(−32x+38)×3
Apply the distributive property
−32x×3+38×3
Simplify
−2x+8
3y−15=−2x+8
Move the expression to the left side
3y−15+2x=8
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
3sin(θ)×r−15+2cos(θ)×r=8
Factor the expression
(3sin(θ)+2cos(θ))r−15=8
Subtract the terms
(3sin(θ)+2cos(θ))r−15−(−15)=8−(−15)
Evaluate
(3sin(θ)+2cos(θ))r=23
Solution
r=3sin(θ)+2cos(θ)23
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−32
Calculate
y−5=−32(x−4)
Simplify the expression
y−5=−32x+38
Take the derivative of both sides
dxd(y−5)=dxd(−32x+38)
Calculate the derivative
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Evaluate
dxd(y−5)
Use differentiation rules
dxd(y)+dxd(−5)
Evaluate the derivative
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Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy+dxd(−5)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(−32x+38)
Solution
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Evaluate
dxd(−32x+38)
Use differentiation rules
dxd(−32x)+dxd(38)
Evaluate the derivative
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Evaluate
dxd(−32x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−32×dxd(x)
Use dxdxn=nxn−1 to find derivative
−32×1
Any expression multiplied by 1 remains the same
−32
−32+dxd(38)
Use dxd(c)=0 to find derivative
−32+0
Evaluate
−32
dxdy=−32
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
y−5=−32(x−4)
Simplify the expression
y−5=−32x+38
Take the derivative of both sides
dxd(y−5)=dxd(−32x+38)
Calculate the derivative
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Evaluate
dxd(y−5)
Use differentiation rules
dxd(y)+dxd(−5)
Evaluate the derivative
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Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy+dxd(−5)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(−32x+38)
Calculate the derivative
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Evaluate
dxd(−32x+38)
Use differentiation rules
dxd(−32x)+dxd(38)
Evaluate the derivative
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Evaluate
dxd(−32x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−32×dxd(x)
Use dxdxn=nxn−1 to find derivative
−32×1
Any expression multiplied by 1 remains the same
−32
−32+dxd(38)
Use dxd(c)=0 to find derivative
−32+0
Evaluate
−32
dxdy=−32
Take the derivative of both sides
dxd(dxdy)=dxd(−32)
Calculate the derivative
dx2d2y=dxd(−32)
Solution
dx2d2y=0
Show Solution
