Hi there! Thank you for the opportunity to help you with your question!

The equation you have here is the equation of a line. This means that, for any value of x that you choose, there will be a corresponding value of y that goes along with it. For example, if I pick the point x = 0, then we would have 0 + 4y = 27. This tells us that y = 27/4, or y = 6.75. You can keep finding other points, for example, when x = 3:

3+4y = 27

4y = 27-3

4y = 24

y = 6.

So now we know that the points (x=0, y = 6.75) and (x=3, y =6) are both solutions to this equation. We can keep going, plotting more and more points, but this information is actually enough to plot ALL the solutions! They would look like this:

A line that goes through the points (0,6.75) and (3, 6).

Another way to solve this, is to isolate y:

x + 4y = 27 [now we subtract x from both sides:]

4y = -x + 27 [and now we divide both sides by 4:]

y = -x/4 + 27/4

This is called the slope intercept form, because the equation immediately tells the slope as the coefficient multiplying x, in this case -1/4, and the y-intercept, in this case 27/4

Please let me know if you need any clarification. Always glad to help!

Aug 31st, 2015

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