# Coordinate geometry-22

### From Homeworkwiki

**If the line ax - y = 6 and 4x + (a + 4)y = -6 are parallel, what is a?**

**Solution:** When 2 lines are parallel to each other, their slopes are equal. Slope of a line is given by dy/dx

1st line : ax - y = 6

=> y = ax - 6

So, dy/dx = a

2nd line : 4x + (a + 4)y = -6

=> (a + 4)y = -4x - 6

=> y = (-4/(a+4))x - 6/(a+4)

So, dy/dx = -4/(a+4)

Their slopes are equal

So, a = -4/(a+4)

=> a * (a+4) = -4

=> a^{2}+ 4a + 4 = 0

=> (a + 2)*(a + 2) = 0

i.e. a = -2