When will the lines be parallel?

R

Redinorun

New member
Joined
May 13, 2014
Messages
3
For which "a" will the line (2a - a²)x - y + a = 0, be parallel with line y = -3x? Can't figure it out. Please help!

Thank You!

(I alredy figured that because of the the fact that they have to have same coefficients to be parallel it has to be 2a - a² = -3. But how to solve this? Correct me if I'm wrong please.)
 
Redinorun said:
For which "a" will the line (2a - a²)x - y + a = 0, be parallel with line y = -3x? Can't figure it out. Please help!

Thank You!

(I alredy figured that because of the the fact that they have to have same coefficients to be parallel it has to be 2a - a² = -3. But how to solve this? Correct me if I'm wrong please.)
Click to expand...

Correct...

2a - a2 = -3

a2 - 2a - 3 = 0

This is a quadratic equation - you can solve it by using factorization or quadratic formula.
 
Last edited by a moderator:
Redinorun said:
For which "a" will the line (2a - a²)x - y + a = 0, be parallel with line y = -3x? Can't figure it out. Please help!

Thank You!

(I alredy figured that because of the the fact that they have to have same coefficients to be parallel it has to be 2a - a² = -3. But how to solve this? Correct me if I'm wrong please.)
Click to expand...
Good! The two lines will be parallel if their "slopes" are the same: \(\displaystyle 2a- a^2= -3\).

Do you not see that this is the same as the quadratic equation \(\displaystyle a^2 - 2a - 3= 0\)? You should have learned to solve quadratic equations by (a) factoring, (b) completing the square, and (c) the quadratic formula.

"Completing the square" and the "quadratic formula" can always be used. "Factoring" (with integer coefficients) is not always possible but is simplest when it is.
 
Last edited by a moderator:
HallsofIvy said:
Good! The two lines will be parallel if their "slopes" are the same: \(\displaystyle 2a- a^2= -3\).

Do you not see that this is the same as the quadratic equation \(\displaystyle a^2- 2a- 3= 0\)? You should have learned to solve quadratic equations by (a) factoring, (b) completing the square, and (c) the quadratic formula.

"Completing the square" and the "quadratic formula" can always be used. "Factoring" (with integer coefficients) is not always possible but is simplest when it is.
Click to expand...

The problem is we have not learned the quadratic formula yet, and I have no idea how to do this any other way.
 
\(\displaystyle a^2- 2a- 3\) factors very easily. There are only two ways to factor -3 into integer factors. Try them!
 
You must log in or register to reply here.
Top