2x+32y=2

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

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

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

Add -43 and 43.

f(1)=0

The final answer is 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

Add 0 and 43.

f(0)=43

The final answer is 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