# Graph 6x+9y=-54

6x+9y=-54
Solve for y.
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
Rewrite in slope-intercept form.
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
Use the slope-intercept form to find the slope and y-intercept.
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
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 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
-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
-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