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?

Mathematics · High School · Thu Feb 04 2021

llm

Answered on Tue May 31 2022

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

y= -⅔x …….….….. (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

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

b = 10 m - 13

= 10x 3/2 -13

= 15-13

or, b = 2

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