 # A linear equation is an equation in which each term is either a constant or the product of a constant and a single variable. An example of a linear equation is 2x + 3 = 5. In this example, the term 2x is the only term that is not multiplied by a single variable. Every term in the equation is a product of a constant and a single variable.

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So in this example were being asked to graft the equation. Two X minus 12 minus three Y equals zero and notice This is not an equation in standard form or slope intercept form or even in function notation. So, in order to graft this equation, what we need to do is rewrite this either in standard form or slope intercept form. And you can really do any method that you'd like. It really becomes what methods you find easier. Now if I'm looking at this equation two X minus 12 minus three Y. I could put this in standard form if I was to move that negative 12 over to the right hand side. So how would I move it? Well, I would simply add 12 toe both sides of our equation because negative 12 plus 12 0. So those were canceled. So then I will be loved with two x minus three Y is equal to 12. So now take a look. This equation is in standard form, so why don't we go ahead and practice graphing in standard form? Remember, the first thing we need to dio is fine. The X intercept. So remember to find the X intercept. We're going to substitute zero in place of Y and solve for X. So we're gonna have to x minus three times zero is equal to 12. Well, three times zero is zero. So that cancels. So we have two X is equal to 12. So the solve for X, we divide both sides by two, and we find the X is equal to six. So that means we have X intercept to six. So on our x axis, we're going to go over the positive six and put a point. Okay, The next thing we need to dio is find our y intercept. So remember to find the y intercept for an equation, we're simply going to substitute zero in place of X and solve for why? So when we do that, we'll have to time zero minus three. Y is equal to 12. So now we just have to solve this equation for why? Well, two times zero is zero. So this cancels. So we're left with negative three y is equal to 12. So the salt for why we divide both sides by negative three and we find that why is equal to negative four So now we have our Y intercept. It's negative four. So if we go back to our graph on our Y, axis will go down to negative four and put a point. And now that we have both are X and y at Why intercepts graft now to graph the line, we just have to graft the line that goes through both of these points. And don't forget to extend it because graphs go want infinitely. So as you can see one way the graft this equation was to just put in slow into standard form and then find the X and Y intercepts. Syracuse University
##### Top Algebra Educators ##### Heather Z.

Oregon State University   ##### Michael J.

Idaho State University