Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=4
Evaluate
4y=12−3x
To find the x-intercept,set y=0
4×0=12−3x
Any expression multiplied by 0 equals 0
0=12−3x
Swap the sides of the equation
12−3x=0
Move the constant to the right-hand side and change its sign
−3x=0−12
Removing 0 doesn't change the value,so remove it from the expression
−3x=−12
Change the signs on both sides of the equation
3x=12
Divide both sides
33x=312
Divide the numbers
x=312
Solution
More Steps

Evaluate
312
Reduce the numbers
14
Calculate
4
x=4
Show Solution

Solve the equation
Solve for x
Solve for y
x=3−4y+12
Evaluate
4y=12−3x
Swap the sides of the equation
12−3x=4y
Move the constant to the right-hand side and change its sign
−3x=4y−12
Change the signs on both sides of the equation
3x=−4y+12
Divide both sides
33x=3−4y+12
Solution
x=3−4y+12
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=12−3x
To test if the graph of 4y=12−3x is symmetry with respect to the origin,substitute -x for x and -y for y
4(−y)=12−3(−x)
Evaluate
−4y=12−3(−x)
Evaluate
More Steps

Evaluate
12−3(−x)
Multiply the numbers
12−(−3x)
Rewrite the expression
12+3x
−4y=12+3x
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)12
Evaluate
4y=12−3x
Move the expression to the left side
4y+3x=12
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
4sin(θ)×r+3cos(θ)×r=12
Factor the expression
(4sin(θ)+3cos(θ))r=12
Solution
r=4sin(θ)+3cos(θ)12
Show Solution

Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−43
Calculate
4y=12−3x
Take the derivative of both sides
dxd(4y)=dxd(12−3x)
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(12−3x)
Calculate the derivative
More Steps

Evaluate
dxd(12−3x)
Use differentiation rules
dxd(12)+dxd(−3x)
Use dxd(c)=0 to find derivative
0+dxd(−3x)
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
0−3
Evaluate
−3
4dxdy=−3
Divide both sides
44dxdy=4−3
Divide the numbers
dxdy=4−3
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=12−3x
Take the derivative of both sides
dxd(4y)=dxd(12−3x)
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(12−3x)
Calculate the derivative
More Steps

Evaluate
dxd(12−3x)
Use differentiation rules
dxd(12)+dxd(−3x)
Use dxd(c)=0 to find derivative
0+dxd(−3x)
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
0−3
Evaluate
−3
4dxdy=−3
Divide both sides
44dxdy=4−3
Divide the numbers
dxdy=4−3
Use b−a=−ba=−ba to rewrite the fraction
dxdy=−43
Take the derivative of both sides
dxd(dxdy)=dxd(−43)
Calculate the derivative
dx2d2y=dxd(−43)
Solution
dx2d2y=0
Show Solution
