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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
where, a and b are x and y intercepts respectively.
Multiply both sides by 24.
Slope intercept form is
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,
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 .