3x+9y-12=0

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

Subtract 3x from both sides of the equation.

9y-12=-3x

Add 12 to both sides of the equation.

9y=-3x+12

9y=-3x+12

Divide each term by 9 and simplify.

Divide each term in 9y=-3x+12 by 9.

9y9=-3×9+129

Cancel the common factor of 9.

Cancel the common factor.

9y9=-3×9+129

Divide y by 1.

y=-3×9+129

y=-3×9+129

Simplify each term.

Cancel the common factor of -3 and 9.

Factor 3 out of -3x.

y=3(-x)9+129

Cancel the common factors.

Factor 3 out of 9.

y=3(-x)3(3)+129

Cancel the common factor.

y=3(-x)3⋅3+129

Rewrite the expression.

y=-x3+129

y=-x3+129

y=-x3+129

Move the negative in front of the fraction.

y=-x3+129

Cancel the common factor of 12 and 9.

Factor 3 out of 12.

y=-x3+3(4)9

Cancel the common factors.

Factor 3 out of 9.

y=-x3+3⋅43⋅3

Cancel the common factor.

y=-x3+3⋅43⋅3

Rewrite the expression.

y=-x3+43

y=-x3+43

y=-x3+43

y=-x3+43

y=-x3+43

y=-x3+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=-13

b=43

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

Slope: -13

y-intercept: 43

Slope: -13

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)=-13+43

Simplify the result.

Combine the numerators over the common denominator.

f(1)=-1+43

Add -1 and 4.

f(1)=33

Divide 3 by 3.

f(1)=1

The final answer is 1.

1

1

The y value at x=1 is 1.

y=1

y=1

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

Replace the variable x with 0 in the expression.

f(0)=-03+43

Simplify the result.

Combine the numerators over the common denominator.

f(0)=0+43

Add 0 and 4.

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.

xy04311

xy04311

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

Slope: -13

y-intercept: 43

xy04311

Graph 3x+9y-12=0