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The given equation is 3x + 9y = -18. To correctly graph the equation, it would be helpful to write the equation in its slope-intercept form which is expressed as:

y = mx + b where m is the slope and b is the y value when x is 0 or the y-intercept.

3x + 9y = -18
9y= -3x -18 
y= -1/3x - 2

Therefore, the slope would be -1/3 and the y-intercept is -2. You use these data to graph the equation.

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Answer:

The graph in the attached figure

Step-by-step explanation:

we have

\(3x+9y=-18\)

Isolate the variable y

\(9y=-3x-18\)

Divide by \(9\) both sides

\(y=-(1/3)x-2\)

The slope of the line is negative  \(m=-\frac{1}{3}\)

The y-intercept is equal to the point \((0,-2)\) (value of y when the value of x is equal to zero)

The x-intercept is equal to the point \((-6,0)\) (value of x when the value of y is equal to zero)

Plot the intercepts to graph the line

see the attached figure

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