Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=425
Evaluate
−3y=25−4x
To find the x-intercept,set y=0
−3×0=25−4x
Any expression multiplied by 0 equals 0
0=25−4x
Swap the sides of the equation
25−4x=0
Move the constant to the right-hand side and change its sign
−4x=0−25
Removing 0 doesn't change the value,so remove it from the expression
−4x=−25
Change the signs on both sides of the equation
4x=25
Divide both sides
44x=425
Solution
x=425
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Solve the equation
Solve for x
Solve for y
x=43y+25
Evaluate
−3y=25−4x
Swap the sides of the equation
25−4x=−3y
Move the constant to the right-hand side and change its sign
−4x=−3y−25
Change the signs on both sides of the equation
4x=3y+25
Divide both sides
44x=43y+25
Solution
x=43y+25
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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
−3y=25−4x
To test if the graph of −3y=25−4x is symmetry with respect to the origin,substitute -x for x and -y for y
−3(−y)=25−4(−x)
Evaluate
3y=25−4(−x)
Evaluate
More Steps

Evaluate
25−4(−x)
Multiply the numbers
25−(−4x)
Rewrite the expression
25+4x
3y=25+4x
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=−3sin(θ)+4cos(θ)25
Evaluate
−3y=25−4x
Move the expression to the left side
−3y+4x=25
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
−3sin(θ)×r+4cos(θ)×r=25
Factor the expression
(−3sin(θ)+4cos(θ))r=25
Solution
r=−3sin(θ)+4cos(θ)25
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Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=34
Calculate
−3y=25−4x
Take the derivative of both sides
dxd(−3y)=dxd(25−4x)
Calculate the derivative
More Steps

Evaluate
dxd(−3y)
Use differentiation rules
dyd(−3y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(−3y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dyd(y)
Use dxdxn=nxn−1 to find derivative
−3×1
Any expression multiplied by 1 remains the same
−3
−3dxdy
−3dxdy=dxd(25−4x)
Calculate the derivative
More Steps

Evaluate
dxd(25−4x)
Use differentiation rules
dxd(25)+dxd(−4x)
Use dxd(c)=0 to find derivative
0+dxd(−4x)
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
0−4
Evaluate
−4
−3dxdy=−4
Change the signs on both sides of the equation
3dxdy=4
Divide both sides
33dxdy=34
Solution
dxdy=34
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
−3y=25−4x
Take the derivative of both sides
dxd(−3y)=dxd(25−4x)
Calculate the derivative
More Steps

Evaluate
dxd(−3y)
Use differentiation rules
dyd(−3y)×dxdy
Evaluate the derivative
More Steps

Evaluate
dyd(−3y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−3×dyd(y)
Use dxdxn=nxn−1 to find derivative
−3×1
Any expression multiplied by 1 remains the same
−3
−3dxdy
−3dxdy=dxd(25−4x)
Calculate the derivative
More Steps

Evaluate
dxd(25−4x)
Use differentiation rules
dxd(25)+dxd(−4x)
Use dxd(c)=0 to find derivative
0+dxd(−4x)
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
0−4
Evaluate
−4
−3dxdy=−4
Change the signs on both sides of the equation
3dxdy=4
Divide both sides
33dxdy=34
Divide the numbers
dxdy=34
Take the derivative of both sides
dxd(dxdy)=dxd(34)
Calculate the derivative
dx2d2y=dxd(34)
Solution
dx2d2y=0
Show Solution
