Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
y=−4x−3y
To find the x-intercept,set y=0
0=−4x−3×0
Any expression multiplied by 0 equals 0
0=−4x−0
Removing 0 doesn't change the value,so remove it from the expression
0=−4x
Swap the sides of the equation
−4x=0
Change the signs on both sides of the equation
4x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=−y
Evaluate
y=−4x−3y
Swap the sides of the equation
−4x−3y=y
Move the expression to the right-hand side and change its sign
−4x=y+3y
Add the terms
−4x=4y
Change the signs on both sides of the equation
4x=−4y
Divide both sides
44x=4−4y
Divide the numbers
x=4−4y
Solution
More Steps
Evaluate
4−4y
Reduce the numbers
1−y
Calculate
−y
x=−y
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
Symmetry with respect to the origin
Evaluate
y=−4x−3y
To test if the graph of y=−4x−3y is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−4(−x)−3(−y)
Evaluate
More Steps
Evaluate
−4(−x)−3(−y)
Multiply the numbers
4x−3(−y)
Multiply the numbers
4x−(−3y)
Rewrite the expression
4x+3y
−y=4x+3y
Solution
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=0θ=43π+kπ,k∈Z
Evaluate
y=−4x−3y
Move the expression to the left side
4y+4x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4sin(θ)×r+4cos(θ)×r=0
Factor the expression
(4sin(θ)+4cos(θ))r=0
Separate into possible cases
r=04sin(θ)+4cos(θ)=0
Solution
More Steps
Evaluate
4sin(θ)+4cos(θ)=0
Move the expression to the right side
4cos(θ)=0−4sin(θ)
Subtract the terms
4cos(θ)=−4sin(θ)
Divide both sides
sin(θ)4cos(θ)=−4
Divide the terms
More Steps
Evaluate
sin(θ)4cos(θ)
Rewrite the expression
4sin−1(θ)cos(θ)
Rewrite the expression
4cot(θ)
4cot(θ)=−4
Multiply both sides of the equation by 41
4cot(θ)×41=−4×41
Calculate
cot(θ)=−4×41
Calculate
More Steps
Evaluate
−4×41
Reduce the numbers
−1×1
Simplify
−1
cot(θ)=−1
Use the inverse trigonometric function
θ=arccot(−1)
Calculate
θ=43π
Add the period of kπ,k∈Z to find all solutions
θ=43π+kπ,k∈Z
r=0θ=43π+kπ,k∈Z
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−1
Calculate
y=−4x−3y
Take the derivative of both sides
dxd(y)=dxd(−4x−3y)
Calculate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy=dxd(−4x−3y)
Calculate the derivative
More Steps
Evaluate
dxd(−4x−3y)
Use differentiation rules
dxd(−4x)+dxd(−3y)
Evaluate the derivative
More Steps
Evaluate
dxd(−4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−4×dxd(x)
Use dxdxn=nxn−1 to find derivative
−4×1
Any expression multiplied by 1 remains the same
−4
−4+dxd(−3y)
Evaluate the derivative
More Steps
Evaluate
dxd(−3y)
Use differentiation rules
dyd(−3y)×dxdy
Evaluate the derivative
−3dxdy
−4−3dxdy
dxdy=−4−3dxdy
Move the variable to the left side
dxdy+3dxdy=−4
Add the terms
More Steps
Evaluate
dxdy+3dxdy
Collect like terms by calculating the sum or difference of their coefficients
(1+3)dxdy
Add the numbers
4dxdy
4dxdy=−4
Divide both sides
44dxdy=4−4
Divide the numbers
dxdy=4−4
Solution
More Steps
Evaluate
4−4
Reduce the numbers
1−1
Calculate
−1
dxdy=−1
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=−4x−3y
Take the derivative of both sides
dxd(y)=dxd(−4x−3y)
Calculate the derivative
More Steps
Evaluate
dxd(y)
Use differentiation rules
dyd(y)×dxdy
Use dxdxn=nxn−1 to find derivative
dxdy
dxdy=dxd(−4x−3y)
Calculate the derivative
More Steps
Evaluate
dxd(−4x−3y)
Use differentiation rules
dxd(−4x)+dxd(−3y)
Evaluate the derivative
More Steps
Evaluate
dxd(−4x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−4×dxd(x)
Use dxdxn=nxn−1 to find derivative
−4×1
Any expression multiplied by 1 remains the same
−4
−4+dxd(−3y)
Evaluate the derivative
More Steps
Evaluate
dxd(−3y)
Use differentiation rules
dyd(−3y)×dxdy
Evaluate the derivative
−3dxdy
−4−3dxdy
dxdy=−4−3dxdy
Move the variable to the left side
dxdy+3dxdy=−4
Add the terms
More Steps
Evaluate
dxdy+3dxdy
Collect like terms by calculating the sum or difference of their coefficients
(1+3)dxdy
Add the numbers
4dxdy
4dxdy=−4
Divide both sides
44dxdy=4−4
Divide the numbers
dxdy=4−4
Divide the numbers
More Steps
Evaluate
4−4
Reduce the numbers
1−1
Calculate
−1
dxdy=−1
Take the derivative of both sides
dxd(dxdy)=dxd(−1)
Calculate the derivative
dx2d2y=dxd(−1)
Solution
dx2d2y=0
Show Solution
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