

Line Intersection
Given two planar lines with equations in the slopeintercept form \(y=mx+b\), we can find the point where these lines intersect by
finding the point where both equations are equal. We could do this by setting the equations equal to each other, then rearrange to
solve for \(x\) by working the order of operations backwards, but I prefer using polynomial subtraction; I find it to be quicker and
easier than doing it longhand.
Note:This method of determining line intersection cannot be used if either of the lines is vertical (has an infinite slope). This is because a vertical line cannot be represented in slopeintercept form. Instead, since a vertcal line has \(y=\{ℝ\}\), it has an equation of \(x=n\), where \(n\) is the xcoordinate of the line. Simply plug the \(x\) value into the second line's equation and solve for \(y\). 

Analytic Geometry: Lines  Analytic Geometry: Vectors 