# Graph 2x+3/2y=2

2x+32y=2
Solve for y.
Subtract 2x from both sides of the equation.
3y2=2-2x
Multiply both sides of the equation by 23.
23⋅3y2=23⋅(2-2x)
Simplify both sides of the equation.
Simplify 23⋅3y2.
Cancel the common factor of 2.
Cancel the common factor.
23⋅3y2=23⋅(2-2x)
Rewrite the expression.
13⋅(3y)=23⋅(2-2x)
13⋅(3y)=23⋅(2-2x)
Cancel the common factor of 3.
Factor 3 out of 3y.
13⋅(3(y))=23⋅(2-2x)
Cancel the common factor.
13⋅(3y)=23⋅(2-2x)
Rewrite the expression.
y=23⋅(2-2x)
y=23⋅(2-2x)
y=23⋅(2-2x)
Simplify 23⋅(2-2x).
Apply the distributive property.
y=23⋅2+23(-2x)
Multiply 23⋅2.
Combine 23 and 2.
y=2⋅23+23(-2x)
Multiply 2 by 2.
y=43+23(-2x)
y=43+23(-2x)
Multiply 23(-2x).
Combine -2 and 23.
y=43+-2⋅23x
Multiply -2 by 2.
y=43+-43x
Combine -43 and x.
y=43+-4×3
y=43+-4×3
Move the negative in front of the fraction.
y=43-4×3
y=43-4×3
y=43-4×3
Reorder 43 and -4×3.
y=-4×3+43
y=-4×3+43
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=-43
b=43
The slope of the line is the value of m, and the y-intercept is the value of b.
Slope: -43
y-intercept: 43
Slope: -43
y-intercept: 43
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 1 to substitute in for x to find the ordered pair.
Replace the variable x with 1 in the expression.
f(1)=-4(1)3+43
Simplify the result.
Multiply 4 by 1.
f(1)=-43+43
f(1)=0
0
0
The y value at x=1 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)=-4(0)3+43
Simplify the result.
Simplify each term.
Cancel the common factor of 0 and 3.
Factor 3 out of 4(0).
f(0)=-3(4⋅(0))3+43
Cancel the common factors.
Factor 3 out of 3.
f(0)=-3(4⋅(0))3(1)+43
Cancel the common factor.
f(0)=-3(4⋅(0))3⋅1+43
Rewrite the expression.
f(0)=-4⋅(0)1+43
Divide 4⋅(0) by 1.
f(0)=-(4⋅(0))+43
f(0)=-(4⋅(0))+43
f(0)=-(4⋅(0))+43
Multiply 4 by 0.
f(0)=-0+43
Multiply -1 by 0.
f(0)=0+43
f(0)=0+43
f(0)=43
43
43
The y value at x=0 is 43.
y=43
y=43
Create a table of the x and y values.
xy04310
xy04310
Graph the line using the slope and the y-intercept, or the points.
Slope: -43
y-intercept: 43
xy04310
Graph 2x+3/2y=2