Line

[Squexy]

Could anyone give me some tips on how to solve these questions?

(1) The equation of the line which passes through \(\displaystyle (-3,\, 2)\) and is orthogonal to the line \(\displaystyle 3x\, -\, 4y\, -\, 12\, =\, 0\) is given by:

. . .(a) ___ \(\displaystyle x\, +\, \)(b) ___ \(\displaystyle y\, +\, 1\, =\, 0\)

(2) If \(\displaystyle x\, =\, \dfrac{\sqrt{5\, }\, -\, 1}{2},\) then \(\displaystyle x^3\, +\, x\, +\, 1\, =\, \) ___

I don´t know how to begin in the first one, tried to do the second one and got 32 √5 - 7/18 as an answer

 

[HallsofIvy]

Could anyone give me some tips on how to solve these questions?

(1) The equation of the line which passes through \(\displaystyle (-3,\, 2)\) and is orthogonal to the line \(\displaystyle 3x\, -\, 4y\, -\, 12\, =\, 0\) is given by:

. . .(a) ___ \(\displaystyle x\, +\, \)(b) ___ \(\displaystyle y\, +\, 1\, =\, 0\)

(2) If \(\displaystyle x\, =\, \dfrac{\sqrt{5\, }\, -\, 1}{2},\) then \(\displaystyle x^3\, +\, x\, +\, 1\, =\, \) ___

I don´t know how to begin in the first one, tried to do the second one and got 32 √5 - 7/18 as an answer

For the first one, a line with slope m, through point (a, b) has equation y= m(x- a)+ b. Further a line perpendicular to y= mx+ b has slope -1/m.

As for the second one, that is not at all what I get. What did you get for \(\displaystyle x^3\)?