Question

In the x-y plane l has a y-intercept of -13 and is perpendicular to the line with equation y= -2/3x.If the point (10,b) is on the line l, what is the value of b?

Answer 1

In the given point (10,b),  the value of b = 2.

Step-by-step explanation:

Here, the  equation of the line perpendicular to line l  is given as:

$y = -(\frac{2}{3}) x$    ..... (1)

The y - intercept of l is given as: - 13

The point on l = (10,b)

Now, the equation of line with point (10,b) and y intercept as - 13 is given as:

y = m x + C  : (x,y) is point on line and C is y- intercept

So, the equation of line l is given as:

b =  m (10)  +  (-13)

or, b = 10 m - 13    .. (2)

As given (1) and (2) are perpendicular.

So, slope of line 1 x Slope of line l =  -1

$\implies (-\frac{2}{3} ) \times m = -1\\\implies m = (\frac{3}{2})$

Putting this value of m in (2), we get:

b = 10 m - 13  =  $10\times (\frac{3}{2}) - 13 = 15 - 13 = 2$

or, b = 2

Hence, in the given point (10,b) the value of b = 2.