Answer:
[tex]y=-\dfrac{1}{3}x+4[/tex]
Step-by-step explanation:
Slope of line with given x and y intercepts
The x-intercept is when y = 0.
Therefore, if the x-intercept is 5 ⇒ (5, 0).
The y-intercept is when x = 0.
Therefore, the y-intercept is -15 ⇒ (0, -15).
Inputting these two points into the slope formula to find the slope of this line:
[tex]\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{-15-0}{0-5}=3[/tex]
Slope of function f(x)
If the function f(x) is perpendicular to the above line, then the slope of function f(x) is the negative reciprocal of the slope of the line.
[tex]\implies \sf slope\:of\:f(x)=-\dfrac{1}{3}[/tex]
Equation of f(x) in point-slope form
Use the found slope and the point (-6, 6) with the point-slope form of a linear equation to find the equation of function f(x):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x-(-6))[/tex]
[tex]\implies y-6=-\dfrac{1}{3}(x+6)[/tex]
Expand and rearrange so that the equation is in the slope-intercept form of y=mx+b:
[tex]\implies y-6=-\dfrac{1}{3}x-2[/tex]
[tex]\implies y=-\dfrac{1}{3}x+4[/tex]
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