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how do I graph a Linear Inequality if Y is by itself and x is with fractions and regular numbers

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Hi Jake;
If there was no equal sign, you will use a dotted line.
Because of the equal sign, you will use a non-dotted line.
y <= -4/9 x - 3
We already know one point on the line.  It is the y-intercept, (0,-3).  We know this because the equation is in slope-intercept format...
y=mx+b
m is the slope, -4/9.
b is the y-intercept.
Begin with the y-intercept.  Then, the slope will function as 4/-9.  You will move up, positively, 4 points on the y-axis, and then to the left, negatively, 9 points on the x-axis.  Then extend the line.  Then, you will shade the area to the left.