Given:
The graph of f passes through (-6,9).
It is perpendicular to the line that has an x-intercept of 8 and a y-intercept of -24.
To find:
The equation of the function f.
Solution:
The equation of line on which graph of f is perpendicular, is
![\dfrac{x}{a}+\dfrac{y}{b}=1](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7Ba%7D%2B%5Cdfrac%7By%7D%7Bb%7D%3D1)
where, a and b are x and y intercepts respectively.
![\dfrac{x}{8}+\dfrac{y}{-24}=1](https://tex.z-dn.net/?f=%5Cdfrac%7Bx%7D%7B8%7D%2B%5Cdfrac%7By%7D%7B-24%7D%3D1)
Multiply both sides by 24.
![3x-y=24](https://tex.z-dn.net/?f=3x-y%3D24)
Slope intercept form is
![y=3x-24](https://tex.z-dn.net/?f=y%3D3x-24)
Slope of this line is 3 and y-intercept is -24.
Product of slopes of two perpendicular lines is -1.
Let the slope of f is m. So,
![m\times 3=-1](https://tex.z-dn.net/?f=m%5Ctimes%203%3D-1)
![m=-\dfrac{1}{3}](https://tex.z-dn.net/?f=m%3D-%5Cdfrac%7B1%7D%7B3%7D)
Slope of m is -1/3 and it passes through (-6,9). So, the equation of function f is
Put y=f(x).
Therefore, the required function is
.