Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=−6
Evaluate
−4y=−3x−18
To find the x-intercept,set y=0
−4×0=−3x−18
Any expression multiplied by 0 equals 0
0=−3x−18
Swap the sides of the equation
−3x−18=0
Move the constant to the right-hand side and change its sign
−3x=0+18
Removing 0 doesn't change the value,so remove it from the expression
−3x=18
Change the signs on both sides of the equation
3x=−18
Divide both sides
33x=3−18
Divide the numbers
x=3−18
Solution
More Steps

Evaluate
3−18
Reduce the numbers
1−6
Calculate
−6
x=−6
Show Solution

Solve the equation
Solve for x
Solve for y
x=34y−18
Evaluate
−4y=−3x−18
Swap the sides of the equation
−3x−18=−4y
Move the constant to the right-hand side and change its sign
−3x=−4y+18
Change the signs on both sides of the equation
3x=4y−18
Divide both sides
33x=34y−18
Solution
x=34y−18
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
−4y=−3x−18
To test if the graph of −4y=−3x−18 is symmetry with respect to the origin,substitute -x for x and -y for y
−4(−y)=−3(−x)−18
Evaluate
4y=−3(−x)−18
Evaluate
4y=3x−18
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)18
Evaluate
−4y=−3x−18
Move the expression to the left side
−4y+3x=−18
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
−4sin(θ)×r+3cos(θ)×r=−18
Factor the expression
(−4sin(θ)+3cos(θ))r=−18
Solution
r=4sin(θ)−3cos(θ)18
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=43
Calculate
−4y=−3x−18
Take the derivative of both sides
dxd(−4y)=dxd(−3x−18)
Calculate the derivative
More Steps

Evaluate
dxd(−4y)
Use differentiation rules
dyd(−4y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(−4y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−4×dyd(y)
Use dxdxn=nxn−1 to find derivative
−4×1
Any expression multiplied by 1 remains the same
−4
−4dxdy
−4dxdy=dxd(−3x−18)
Calculate the derivative
More Steps

Evaluate
dxd(−3x−18)
Use differentiation rules
dxd(−3x)+dxd(−18)
Evaluate the derivative
More Steps

Evaluate
dxd(−3x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dxd(x)
Use dxdxn=nxn−1 to find derivative
−3×1
Any expression multiplied by 1 remains the same
−3
−3+dxd(−18)
Use dxd(c)=0 to find derivative
−3+0
Evaluate
−3
−4dxdy=−3
Change the signs on both sides of the equation
4dxdy=3
Divide both sides
44dxdy=43
Solution
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
−4y=−3x−18
Take the derivative of both sides
dxd(−4y)=dxd(−3x−18)
Calculate the derivative
More Steps

Evaluate
dxd(−4y)
Use differentiation rules
dyd(−4y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(−4y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−4×dyd(y)
Use dxdxn=nxn−1 to find derivative
−4×1
Any expression multiplied by 1 remains the same
−4
−4dxdy
−4dxdy=dxd(−3x−18)
Calculate the derivative
More Steps

Evaluate
dxd(−3x−18)
Use differentiation rules
dxd(−3x)+dxd(−18)
Evaluate the derivative
More Steps

Evaluate
dxd(−3x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dxd(x)
Use dxdxn=nxn−1 to find derivative
−3×1
Any expression multiplied by 1 remains the same
−3
−3+dxd(−18)
Use dxd(c)=0 to find derivative
−3+0
Evaluate
−3
−4dxdy=−3
Change the signs on both sides of the equation
4dxdy=3
Divide both sides
44dxdy=43
Divide the numbers
dxdy=43
Take the derivative of both sides
dxd(dxdy)=dxd(43)
Calculate the derivative
dx2d2y=dxd(43)
Solution
dx2d2y=0
Show Solution
