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.

Explanation:

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

`y = -((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 (-(2)/(3) ) * m = -1\\\implies m = ((3)/(2))`

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

b = 10 m - 13 =
`10* ((3)/(2)) - 13 = 15 - 13 = 2`

or, b = 2

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