Question

The graph of f passes through (-6,9) and is perpendicular to the line that has an x-intercept of 8 and a y-intercept of -24 the equation of the function is?

Answer 1

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

$\dfrac{x}{a}+\dfrac{y}{b}=1$

where, a and b are x and y intercepts respectively.

$\dfrac{x}{8}+\dfrac{y}{-24}=1$

Multiply both sides by 24.

$3x-y=24$

Slope intercept form is

$y=3x-24$

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,

$m\times 3=-1$

$m=-\dfrac{1}{3}$

Slope of m is -1/3 and it passes through (-6,9). So, the equation of function f is

$y-y_1=m(x-x_1)$

$y-9=-\dfrac{1}{3}(x-(-6))$

$y-9=-\dfrac{1}{3}(x+6)$

$y-9=-\dfrac{1}{3}x-2$

$y=-\dfrac{1}{3}x-2+9$

$y=-\dfrac{1}{3}x+7$

Put y=f(x).

$f(x)=-\dfrac{1}{3}x+7$

Therefore, the required function is $f(x)=-\dfrac{1}{3}x+7$.