Question

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.

Answer 1

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`