Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=329
Evaluate
y−2=−43(x−7)
To find the x-intercept,set y=0
0−2=−43(x−7)
Removing 0 doesn't change the value,so remove it from the expression
−2=−43(x−7)
Simplify
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Evaluate
−43(x−7)
Multiply the terms
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Evaluate
43(x−7)
Apply the distributive property
43x−43×7
Multiply the numbers
43x−421
−(43x−421)
Calculate
−43x+421
−2=−43x+421
Swap the sides of the equation
−43x+421=−2
Move the constant to the right-hand side and change its sign
−43x=−2−421
Subtract the numbers
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Evaluate
−2−421
Reduce fractions to a common denominator
−42×4−421
Write all numerators above the common denominator
4−2×4−21
Multiply the numbers
4−8−21
Subtract the numbers
4−29
Use b−a=−ba=−ba to rewrite the fraction
−429
−43x=−429
Change the signs on both sides of the equation
43x=429
Multiply by the reciprocal
43x×34=429×34
Multiply
x=429×34
Solution
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Evaluate
429×34
Reduce the numbers
29×31
Multiply the numbers
329
x=329
Show Solution

Solve the equation
Solve for x
Solve for y
x=3−4y+29
Evaluate
y−2=−43(x−7)
Simplify
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Evaluate
−43(x−7)
Multiply the terms
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Evaluate
43(x−7)
Apply the distributive property
43x−43×7
Multiply the numbers
43x−421
−(43x−421)
Calculate
−43x+421
y−2=−43x+421
Swap the sides of the equation
−43x+421=y−2
Move the constant to the right-hand side and change its sign
−43x=y−2−421
Subtract the terms
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Evaluate
y−2−421
Reduce fractions to a common denominator
4y×4−42×4−421
Write all numerators above the common denominator
4y×4−2×4−21
Use the commutative property to reorder the terms
44y−2×4−21
Multiply the numbers
44y−8−21
Subtract the numbers
44y−29
−43x=44y−29
Change the signs on both sides of the equation
43x=4−4y+29
Multiply by the reciprocal
43x×34=4−4y+29×34
Multiply
x=4−4y+29×34
Solution
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Evaluate
4−4y+29×34
Rewrite the expression
−44y−29×34
Reduce the numbers
−(4y−29)×31
Calculate the product
3−4y+29
x=3−4y+29
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−2=−43(x−7)
Simplify the expression
y−2=−43x+421
To test if the graph of y−2=−43x+421 is symmetry with respect to the origin,substitute -x for x and -y for y
−y−2=−43(−x)+421
Multiplying or dividing an even number of negative terms equals a positive
−y−2=43x+421
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=4sin(θ)+3cos(θ)29
Evaluate
y−2=−43(x−7)
Evaluate
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Evaluate
−43(x−7)
Multiply the terms
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Evaluate
43(x−7)
Apply the distributive property
43x−43×7
Multiply the numbers
43x−421
−(43x−421)
Calculate
−43x+421
y−2=−43x+421
Multiply both sides of the equation by LCD
(y−2)×4=(−43x+421)×4
Simplify the equation
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Evaluate
(y−2)×4
Apply the distributive property
y×4−2×4
Use the commutative property to reorder the terms
4y−2×4
Multiply the numbers
4y−8
4y−8=(−43x+421)×4
Simplify the equation
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Evaluate
(−43x+421)×4
Apply the distributive property
−43x×4+421×4
Simplify
−3x+21
4y−8=−3x+21
Move the expression to the left side
4y−8+3x=21
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4sin(θ)×r−8+3cos(θ)×r=21
Factor the expression
(4sin(θ)+3cos(θ))r−8=21
Subtract the terms
(4sin(θ)+3cos(θ))r−8−(−8)=21−(−8)
Evaluate
(4sin(θ)+3cos(θ))r=29
Solution
r=4sin(θ)+3cos(θ)29
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−43
Calculate
y−2=−43(x−7)
Simplify the expression
y−2=−43x+421
Take the derivative of both sides
dxd(y−2)=dxd(−43x+421)
Calculate the derivative
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Evaluate
dxd(y−2)
Use differentiation rules
dxd(y)+dxd(−2)
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(−2)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(−43x+421)
Solution
More Steps

Evaluate
dxd(−43x+421)
Use differentiation rules
dxd(−43x)+dxd(421)
Evaluate the derivative
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Evaluate
dxd(−43x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−43×dxd(x)
Use dxdxn=nxn−1 to find derivative
−43×1
Any expression multiplied by 1 remains the same
−43
−43+dxd(421)
Use dxd(c)=0 to find derivative
−43+0
Evaluate
−43
dxdy=−43
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−2=−43(x−7)
Simplify the expression
y−2=−43x+421
Take the derivative of both sides
dxd(y−2)=dxd(−43x+421)
Calculate the derivative
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Evaluate
dxd(y−2)
Use differentiation rules
dxd(y)+dxd(−2)
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(−2)
Use dxd(c)=0 to find derivative
dxdy+0
Evaluate
dxdy
dxdy=dxd(−43x+421)
Calculate the derivative
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Evaluate
dxd(−43x+421)
Use differentiation rules
dxd(−43x)+dxd(421)
Evaluate the derivative
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Evaluate
dxd(−43x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−43×dxd(x)
Use dxdxn=nxn−1 to find derivative
−43×1
Any expression multiplied by 1 remains the same
−43
−43+dxd(421)
Use dxd(c)=0 to find derivative
−43+0
Evaluate
−43
dxdy=−43
Take the derivative of both sides
dxd(dxdy)=dxd(−43)
Calculate the derivative
dx2d2y=dxd(−43)
Solution
dx2d2y=0
Show Solution
