Question

the equation of the line that has y-intercept 4 and is perpendicular to the line y =3x - 2​

Answer 1

Answer:

This implies that x2+2ax=4x-4a-13 or x2+2ax-4x+4a+13=0 or x2+(2a-4)x+(4a+13)=0

Since the equation has just on solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that,

(2a-4)2=4.1.(4a+13) or 4a2-16a+16=16a+52 or 4a2-32a-36=0 or a2-8a-9=0 or (a-9)(a+1)=0

So the values of a are -1 and 9.

Step-by-step explanation:

hope this helps u

Answer 2

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This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

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