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 $\displaystyle x^3$?