You can put this solution on YOUR website! One equation is already in slope-intercept form.
The other is in standard form.
Rearrange the one in standard form to get the slope-intercept form.
4x + 9y = -27 <---this one is in standard form
y = -4/9x -9 <---this one is in slope-intercept form
standard form [subtract 4x from both sides] [divide both sides by 9] [rearrange for easy reading]
In slope-intercept form the coefficient of x (in this case, -4/9) is the slope of the line, do both lines have the same slope? (If you said yes, you are correct!)
Do the two equations define lines that are separated by some value? Another way of asking this is: do the two lines have different y-intercepts?
If they do, they are parallel.
If they don't, the two equations define the same line; i.e. there is only one line.
(Here's a graph of these two equations)
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