The lines given by the equation y = 9 - 1/3x and y = mx + b are perpendicular and intersect at a point on the x axis. What is the value of b?

• Since these lines are perpendicular, their product of their gradients is negative one:

• m1 is gradient of first line.

• m2 is gradient of second line.

• since they intersect at a point on x-axis, y = 0

• Considering the first line: y = 9 - ⅓x

point is (27, 0)

• Considering the second line: y = mx + b

answer: evaluate the objective function at each vertex to determine which - and -values, if any, maximize or minimize the function. example: find the minimum value and maximum value of the objective function f ( x , y ) = 4 x + 5 y , subject to the following constraints