For how many ordered pairs of positive integers (x,y) is 2x+3y<6
Rearranging the perpendicular line, we get y = -4x + k, so this line has a slope of -4, so the inverse reciprocal slope is 1/4.
Which means, Line 1 has an equation of y = (1/4)x
Line 1: y = (1/4)x
Line 2: y = -4x + k
Since we know they intersect at (t, t+1), this must be a solution to both equations. Since Line 2 would have infinite solutions (since k is unknown), we choose Line 1 to solve for t.
t+1 = (1/4)t
1 = (-3/4)t
(-4/3) = t
So, t = -4/3