find two possible values of p if the lines px-y+1=0 and 3x+y+1=0 intersect at 45 degrees

I am rusty but I will give it a go.

find two possible values of p if the lines px-y+1=0 and 3x+y+1=0 intersect at 45 degrees

px-y+1=0             y=px+1             gradient =p

this line makes an angle of    atan(p)    with the positive axis    I'll call this  $$\theta_1$$

3x+y+1=0            y=-3x-1            gradient = -3

this line makes an angle of    atan(-3)    with the positive axis     I'll call this  $$\theta_2$$

Now we want

 $$\theta_1-\theta_2 = \pm \frac{\pi}{4}$$

You need to use the last formula, do you think you can try to take it from here :)

I like how you did this one, Melody.......{I was "rusty" on this, as well}

Thanks Chris