x6+2-3×6-3y-x6

Factor the equation.

To write -x2 as a fraction with a common denominator, multiply by 33.

x6-x2⋅33+13-3y-x6=0

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

Multiply x2 and 33.

x6-x⋅32⋅3+13-3y-x6=0

Multiply 2 by 3.

x6-x⋅36+13-3y-x6=0

x6-x⋅36+13-3y-x6=0

Combine the numerators over the common denominator.

x-x⋅36+13-3y-x6=0

To write 13 as a fraction with a common denominator, multiply by 22.

x-x⋅36+13⋅22-3y-x6=0

Write each expression with a common denominator of 6, by multiplying each by an appropriate factor of 1.

Multiply 13 and 22.

x-x⋅36+23⋅2-3y-x6=0

Multiply 3 by 2.

x-x⋅36+26-3y-x6=0

x-x⋅36+26-3y-x6=0

Combine the numerators over the common denominator.

x-x⋅3+26-3y-x6=0

Combine the numerators over the common denominator.

x-x⋅3+2-(3y-x)6=0

Rewrite x-x⋅3+2-(3y-x)6 in a factored form.

Multiply 3 by -1.

x-3x+2-(3y-x)6=0

Apply the distributive property.

x-3x+2-(3y)+x6=0

Multiply 3 by -1.

x-3x+2-3y+x6=0

Multiply –x.

Multiply -1 by -1.

x-3x+2-3y+1×6=0

Multiply x by 1.

x-3x+2-3y+x6=0

x-3x+2-3y+x6=0

Subtract 3x from x.

-2x+2-3y+x6=0

Add -2x and x.

-x+2-3y6=0

-x+2-3y6=0

-x+2-3y6=0

Solve the equation.

Multiply both sides of the equation by 6.

-x+2-3y=0⋅(6)

Remove parentheses.

-x+2-3y=0⋅(6)

Multiply 0 by 6.

-x+2-3y=0

Move all terms not containing y to the right side of the equation.

Add x to both sides of the equation.

2-3y=x

Subtract 2 from both sides of the equation.

-3y=x-2

-3y=x-2

Divide each term by -3 and simplify.

Divide each term in -3y=x-2 by -3.

-3y-3=x-3+-2-3

Cancel the common factor of -3.

Cancel the common factor.

-3y-3=x-3+-2-3

Divide y by 1.

y=x-3+-2-3

y=x-3+-2-3

Simplify each term.

Move the negative in front of the fraction.

y=-x3+-2-3

Dividing two negative values results in a positive value.

y=-x3+23

y=-x3+23

y=-x3+23

y=-x3+23

y=-x3+23

The slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

y=mx+b

Find the values of m and b using the form y=mx+b.

m=-13

b=23

The slope of the line is the value of m, and the y-intercept is the value of b.

Slope: -13

y-intercept: 23

Slope: -13

y-intercept: 23

Choose 2 to substitute in for x to find the ordered pair.

Replace the variable x with 2 in the expression.

f(2)=-23+23

Simplify the result.

Add -23 and 23.

f(2)=0

The final answer is 0.

0

0

The y value at x=2 is 0.

y=0

y=0

Choose 0 to substitute in for x to find the ordered pair.

Replace the variable x with 0 in the expression.

f(0)=-03+23

Simplify the result.

Combine the numerators over the common denominator.

f(0)=0+23

Add 0 and 2.

f(0)=23

The final answer is 23.

23

23

The y value at x=0 is 23.

y=23

y=23

Create a table of the x and y values.

xy02320

xy02320

Graph the line using the slope and the y-intercept, or the points.

Slope: -13

y-intercept: 23

xy02320

Graph x/6+(2-3x)/6-(3y-x)/6