Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
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Find all a for which the lines represented by the equations 2y+3+x=0 and 3y+ax+2=0 are perpendicular
Put the first line equation in slope-intercept form:Quote:
Originally Posted by Rimas
2y + 3 + x = 0
y = -(1/2)x - (3/2)
The second line needs to have a slope of +2 to be perpendicular to this line.
Thus:
3y + ax + 2 = 0
y = -(a/3)x - (2/3)
Thus -a/3 = 2. Thus a = -6.
-Dan
If line l_1 has slope m_1 and line l_2 has slope m_2 then if neither line is vertical then the two line are perpendicular if (m_1)(m_2)=-1.Quote:
Originally Posted by Rimas
2y+3+x=0 has slope (-1/2); 3y+ax+2=0 has slope (-a/3).
Now solve for a.