Question

If perpendicular lines m and n intersect at (0,b) in the standard (x,y) coordinate plane, what is the value of b ? (1) the slope of the line m is (2) the point (-1,0) is on line n.

Answer 1

Since slope of line m is 2 so slope of its perpendicular line n must be -1/2. Point (-1,0) is on line n so its Equation...

$y - 0 = - \frac{1}{2} (x + 1) \\ x + 2y + 1= 0$

since (0,b) lie one line n so... satisfy this point with n...

$(0 \: \: b) \: = > \: \: 0 + 2b + 1 = 0 \\ b = - \frac{1}{2}$