16.5k views
5 votes
If perpendicular lines m and n intersect at (0,b) in the standard (x,y) coordinate plane, what is the value of b ? (1) The slope of the line m is \small -\frac{1}{2} (2) The point (-1,0) is on line n.

1 Answer

3 votes

Answer:

The value of b is 2.

Explanation:

Let the equation of line m is,


y=m_1x+c_1

And, line n is,


y=m_2x+c_2

Where,
m_1 and
m_2 are the slope of lines m and n respectively.

Since, line m and n are perpendicular,


m_1* m_2=-1

We have,
m_1=-(1)/(2),


\implies -(1)/(2)* m_2=-1


\implies m_2=2

Thus, the equation of line n is,


y=2x+c_2

Now, the point (-1,0) is on line n,


0=2(-1)+c_2\implies c_2=2

Hence, the equation of line n is,


y=2x+2

Also, lines m and n intersect at (0,b),

⇒ (0,b) is in both lines m and n,


\implies b = 2(0) + 2


\implies b =2

User Riyad
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories