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

Answer:

The value of b is 2.

Step-by-step 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,

$m_1\times m_2=-1$

We have, $m_1=-\frac{1}{2}$,

$\implies -\frac{1}{2}\times m_2=-1$

$\implies m_2=2$

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,

$\implies b = 2(0) + 2$

$\implies b =2$