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

x6+2-3×6-3y-x6
Solve for y.
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
Use the slope-intercept form to find the slope and y-intercept.
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
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
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

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