Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the x-intercept/zero
Find the y-intercept
Find the slope
x=0
Evaluate
y×7=−(x×10)
To find the x-intercept,set y=0
0×7=−(x×10)
Any expression multiplied by 0 equals 0
0=−(x×10)
Use the commutative property to reorder the terms
0=−10x
Swap the sides of the equation
−10x=0
Change the signs on both sides of the equation
10x=0
Solution
x=0
Show Solution
Solve the equation
Solve for x
Solve for y
x=−107y
Evaluate
y×7=−(x×10)
Use the commutative property to reorder the terms
7y=−(x×10)
Use the commutative property to reorder the terms
7y=−10x
Swap the sides of the equation
−10x=7y
Change the signs on both sides of the equation
10x=−7y
Divide both sides
1010x=10−7y
Divide the numbers
x=10−7y
Solution
x=−107y
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
y7=−(x10)
Simplify the expression
7y=−10x
To test if the graph of 7y=−10x is symmetry with respect to the origin,substitute -x for x and -y for y
7(−y)=−10(−x)
Evaluate
−7y=−10(−x)
Evaluate
−7y=10x
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=arccot(−107)+kπ,k∈Z
Evaluate
y×7=−(x×10)
Use the commutative property to reorder the terms
7y=−(x×10)
Use the commutative property to reorder the terms
7y=−10x
Move the expression to the left side
7y+10x=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
7sin(θ)×r+10cos(θ)×r=0
Factor the expression
(7sin(θ)+10cos(θ))r=0
Separate into possible cases
r=07sin(θ)+10cos(θ)=0
Solution
More Steps
Evaluate
7sin(θ)+10cos(θ)=0
Move the expression to the right side
10cos(θ)=0−7sin(θ)
Subtract the terms
10cos(θ)=−7sin(θ)
Divide both sides
sin(θ)10cos(θ)=−7
Divide the terms
More Steps
Evaluate
sin(θ)10cos(θ)
Rewrite the expression
10sin−1(θ)cos(θ)
Rewrite the expression
10cot(θ)
10cot(θ)=−7
Multiply both sides of the equation by 101
10cot(θ)×101=−7×101
Calculate
cot(θ)=−7×101
Multiply the numbers
cot(θ)=−107
Use the inverse trigonometric function
θ=arccot(−107)
Add the period of kπ,k∈Z to find all solutions
θ=arccot(−107)+kπ,k∈Z
r=0θ=arccot(−107)+kπ,k∈Z
Show Solution
Find the first derivative
Find the derivative with respect to x
Find the derivative with respect to y
dxdy=−710
Calculate
y7=−(x10)
Simplify the expression
7y=−10x
Take the derivative of both sides
dxd(7y)=dxd(−10x)
Calculate the derivative
More Steps
Evaluate
dxd(7y)
Use differentiation rules
dyd(7y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(7y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
7×dyd(y)
Use dxdxn=nxn−1 to find derivative
7×1
Any expression multiplied by 1 remains the same
7
7dxdy
7dxdy=dxd(−10x)
Calculate the derivative
More Steps
Evaluate
dxd(−10x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−10×dxd(x)
Use dxdxn=nxn−1 to find derivative
−10×1
Any expression multiplied by 1 remains the same
−10
7dxdy=−10
Divide both sides
77dxdy=7−10
Divide the numbers
dxdy=7−10
Solution
dxdy=−710
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
y7=−(x10)
Simplify the expression
7y=−10x
Take the derivative of both sides
dxd(7y)=dxd(−10x)
Calculate the derivative
More Steps
Evaluate
dxd(7y)
Use differentiation rules
dyd(7y)×dxdy
Evaluate the derivative
More Steps
Evaluate
dyd(7y)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
7×dyd(y)
Use dxdxn=nxn−1 to find derivative
7×1
Any expression multiplied by 1 remains the same
7
7dxdy
7dxdy=dxd(−10x)
Calculate the derivative
More Steps
Evaluate
dxd(−10x)
Use differentiation rule dxd(cf(x))=c×dxd(f(x))
−10×dxd(x)
Use dxdxn=nxn−1 to find derivative
−10×1
Any expression multiplied by 1 remains the same
−10
7dxdy=−10
Divide both sides
77dxdy=7−10
Divide the numbers
dxdy=7−10
Use b−a=−ba=−ba to rewrite the fraction
dxdy=−710
Take the derivative of both sides
dxd(dxdy)=dxd(−710)
Calculate the derivative
dx2d2y=dxd(−710)
Solution
dx2d2y=0
Show Solution
Graph
