The straight line L1 has equation x+2y=4 The straight line L2 passes through the points (-1,-7) and (7,9) Michael says that the lines L1 and L2 are perpendicular Is Michael correct and you must show your working out clearly

Yes

Step-by-step explanation:

The idea is to use the formula for perpendicular gradients,

meaning m1 * m2 = -1

Since L2 passes through 2 points and to find gradient we just need 2 points,

we can use the 2 given points given

L2 gradient is (9 - (-7)) / (7 - (-1)) = 16/8 = 2

x + 2y = 4 rewrite as  y = -(0.5)x + 2

so our m1 is -0.5 and m2 is 2

-0.5 * 2 = -1  which was what we wanted to show.

L1 and L2 are perpendicular