We know that every line can be uniquely determined by two points, say (1, 1) and (2, 2). Recall that the standard equation of a line in 2 is given by + + = 0. If we plug our points into this equation we obtain a system of three equations with three unknowns. + + = 0 1 + 1 + = 0 2 + 2 + = 0 or [ 1 1 1 1 2 2 1 ] [ ] = [ 0 0 0 ] Our proposition tells us this has a nontrivial solution if and only if () | 1 1 1 1 2 2 1 | = 0 2) Use baby algebra to find the slope-intercept equations ( = + ) of the lines through the following pairs of points. a) (1, 1) and (2, 2) b) (0, 1) and (1, 1) 3) For each of the pairs of points above, plug the points into () and take the determinant. What do you notice about the result