How to find where a quadratic formula and linear line intersect. I'm Bon Crowder and we're talking about quadratic equations and linear lines or linear equations and where they run into each other. The important thing to note is the point at which or the points at which they intersect lie on both equations or on the graphs of both equations. So this Y and this Y are the same Y so we can set these equal to each other. So we have X squared - 4X + 5. This is this Y = this Y which is -X + 5. Now, I'm going to put everything on one side, add my X, subtract my 5. I can do this simultaneously. I have X squared - 3X + 0 is 0. So now I need to find out where this equals 0. I can factor out an X and I have X - 3. We have that special property that says that if two things multiply together to give you 0, somebody better be 0. So this one could be 0 or this one can be 0. Solving for X well that one is already done, here we add the 3 and we have X is 0 or X is 3. Well we want the point, not just the X value, so we can plug 0 into either one of these equations and it will give us the same thing. Plug it in over here because it seems nicer and Y = 5, X = 3, plug it in over here, -3 + 5 is 2. So we have the point 0, 5 and the point 3, 2 where these two intersect. Now this was a factor job, this could easily, you could use the quadratic formula on that however it works. But this is how you find where the intersecting point is between a quadratic formula or a quadratic equation and a linear equation. I'm Bon Crowder and that's how you do it, enjoy it.