6x+9y=-54

Subtract 6x from both sides of the equation.

9y=-54-6x

Divide each term by 9 and simplify.

Divide each term in 9y=-54-6x by 9.

9y9=-549+-6×9

Cancel the common factor of 9.

Cancel the common factor.

9y9=-549+-6×9

Divide y by 1.

y=-549+-6×9

y=-549+-6×9

Simplify each term.

Divide -54 by 9.

y=-6+-6×9

Cancel the common factor of -6 and 9.

Factor 3 out of -6x.

y=-6+3(-2x)9

Cancel the common factors.

Factor 3 out of 9.

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

Cancel the common factor.

y=-6+3(-2x)3⋅3

Rewrite the expression.

y=-6+-2×3

y=-6+-2×3

y=-6+-2×3

Move the negative in front of the fraction.

y=-6-2×3

y=-6-2×3

y=-6-2×3

y=-6-2×3

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

y=mx+b

Reorder -6 and -2×3.

y=-2×3-6

Rewrite in slope-intercept form.

y=-23x-6

y=-23x-6

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

m=-23

b=-6

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

Slope: -23

y-intercept: -6

Slope: -23

y-intercept: -6

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

Replace the variable x with 0 in the expression.

f(0)=-2(0)3-6

Simplify the result.

Simplify each term.

Cancel the common factor of 0 and 3.

Factor 3 out of 2(0).

f(0)=-3(2⋅(0))3-6

Cancel the common factors.

Factor 3 out of 3.

f(0)=-3(2⋅(0))3(1)-6

Cancel the common factor.

f(0)=-3(2⋅(0))3⋅1-6

Rewrite the expression.

f(0)=-2⋅(0)1-6

Divide 2⋅(0) by 1.

f(0)=-(2⋅(0))-6

f(0)=-(2⋅(0))-6

f(0)=-(2⋅(0))-6

Multiply 2 by 0.

f(0)=-0-6

Multiply -1 by 0.

f(0)=0-6

f(0)=0-6

Subtract 6 from 0.

f(0)=-6

The final answer is -6.

-6

-6

The y value at x=0 is -6.

y=-6

y=-6

Choose 3 to substitute in for x to find the ordered pair.

Replace the variable x with 3 in the expression.

f(3)=-2(3)3-6

Simplify the result.

Simplify each term.

Cancel the common factor of 3.

Cancel the common factor.

f(3)=-2⋅33-6

Divide 2 by 1.

f(3)=-1⋅2-6

f(3)=-1⋅2-6

Multiply -1 by 2.

f(3)=-2-6

f(3)=-2-6

Subtract 6 from -2.

f(3)=-8

The final answer is -8.

-8

-8

The y value at x=3 is -8.

y=-8

y=-8

Create a table of the x and y values.

xy0-63-8

xy0-63-8

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

Slope: -23

y-intercept: -6

xy0-63-8

Graph 6x+9y=-54