Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=303
Evaluate
1818=6x+9y
To find the x-intercept,set y=0
1818=6x+9×0
Any expression multiplied by 0 equals 0
1818=6x+0
Removing 0 doesn't change the value,so remove it from the expression
1818=6x
Swap the sides of the equation
6x=1818
Divide both sides
66x=61818
Divide the numbers
x=61818
Solution
More Steps

Evaluate
61818
Reduce the numbers
1303
Calculate
303
x=303
Show Solution

Solve the equation
Solve for x
Solve for y
x=2606−3y
Evaluate
1818=6x+9y
Swap the sides of the equation
6x+9y=1818
Move the expression to the right-hand side and change its sign
6x=1818−9y
Divide both sides
66x=61818−9y
Divide the numbers
x=61818−9y
Solution
More Steps

Evaluate
61818−9y
Rewrite the expression
63(606−3y)
Cancel out the common factor 3
2606−3y
x=2606−3y
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
1818=6x+9y
To test if the graph of 1818=6x+9y is symmetry with respect to the origin,substitute -x for x and -y for y
1818=6(−x)+9(−y)
Evaluate
More Steps

Evaluate
6(−x)+9(−y)
Multiply the numbers
−6x+9(−y)
Multiply the numbers
−6x−9y
1818=−6x−9y
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=2cos(θ)+3sin(θ)606
Evaluate
1818=6x+9y
Move the expression to the left side
1818−6x−9y=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
1818−6cos(θ)×r−9sin(θ)×r=0
Factor the expression
(−6cos(θ)−9sin(θ))r+1818=0
Subtract the terms
(−6cos(θ)−9sin(θ))r+1818−1818=0−1818
Evaluate
(−6cos(θ)−9sin(θ))r=−1818
Solution
r=2cos(θ)+3sin(θ)606
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−32
Calculate
1818=6x+9y
Take the derivative of both sides
dxd(1818)=dxd(6x+9y)
Calculate the derivative
0=dxd(6x+9y)
Calculate the derivative
More Steps

Evaluate
dxd(6x+9y)
Use differentiation rules
dxd(6x)+dxd(9y)
Evaluate the derivative
More Steps

Evaluate
dxd(6x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
6×dxd(x)
Use dxdxn=nxn−1 to find derivative
6×1
Any expression multiplied by 1 remains the same
6
6+dxd(9y)
Evaluate the derivative
More Steps

Evaluate
dxd(9y)
Use differentiation rules
dyd(9y)×dxdy
Evaluate the derivative
9dxdy
6+9dxdy
0=6+9dxdy
Swap the sides of the equation
6+9dxdy=0
Move the constant to the right-hand side and change its sign
9dxdy=0−6
Removing 0 doesn't change the value,so remove it from the expression
9dxdy=−6
Divide both sides
99dxdy=9−6
Divide the numbers
dxdy=9−6
Solution
More Steps

Evaluate
9−6
Cancel out the common factor 3
3−2
Use b−a=−ba=−ba to rewrite the fraction
−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
1818=6x+9y
Take the derivative of both sides
dxd(1818)=dxd(6x+9y)
Calculate the derivative
0=dxd(6x+9y)
Calculate the derivative
More Steps

Evaluate
dxd(6x+9y)
Use differentiation rules
dxd(6x)+dxd(9y)
Evaluate the derivative
More Steps

Evaluate
dxd(6x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
6×dxd(x)
Use dxdxn=nxn−1 to find derivative
6×1
Any expression multiplied by 1 remains the same
6
6+dxd(9y)
Evaluate the derivative
More Steps

Evaluate
dxd(9y)
Use differentiation rules
dyd(9y)×dxdy
Evaluate the derivative
9dxdy
6+9dxdy
0=6+9dxdy
Swap the sides of the equation
6+9dxdy=0
Move the constant to the right-hand side and change its sign
9dxdy=0−6
Removing 0 doesn't change the value,so remove it from the expression
9dxdy=−6
Divide both sides
99dxdy=9−6
Divide the numbers
dxdy=9−6
Divide the numbers
More Steps

Evaluate
9−6
Cancel out the common factor 3
3−2
Use b−a=−ba=−ba to rewrite the fraction
−32
dxdy=−32
Take the derivative of both sides
dxd(dxdy)=dxd(−32)
Calculate the derivative
dx2d2y=dxd(−32)
Solution
dx2d2y=0
Show Solution
