Find an equation of the line which is to the given line the

Find an equation of the line which is to the given line the line through (-2,3) with the y-intercept 2.

16. Point( -2 , 3) with y intercept 2 --( 0, 2)

Slope m = (2-3)/( 0- (-2)) = - 1/2

Slope of the line perpendicular to the above line , slope = 2

Std slope intercept equation of line: y = mx +c

y = 2x + c . We have one point ( -2 , 3)

3 = -4 +c ----> c =7

y = 2x +7 ( Solution)

17. 27x^4 + 21x^2 + 4 =0

Let y = x^2:

27y^2 +21y +4 =0

Solve by factorisation: 27y^2 + 12y +9y +4 =0

27y^2 +12y +9y +4 =0

3y (9y +4) +1(9y +4) =0

(3y +1)(9y +4) =0

3y+1 =0 ---> y =-1/3

x^2 = -1/3 ---> x =+ /- i/sqrt3

9y +4 =0 ---> y = -4/9

x^2 = -4/9 ----> x= +/- 2i/3

Solution : x= i/sqrt3 , -i/sqrt3 , 2i/3, -2i/3