Find the slope of the given line.

Question

Suppose you want to find the equation of the line through the point (2, 6) and perpendicular to the line represented by

f(x)= 3x –7.Find the slope of the given line. Call this slope m1. What is m2, the slope of the requested perpendicular line? Show how you use m2 to find the requested result, using either function notation as in the previous problems (f(x) = ___). Use exact fractions, proper or improper, for the slope and y-intercept

Answer 1

perpendicular to f(x) = 3x-7 through (2,6)

 

f(x) is in slope intercept form of y=mx + b  where y represents f(x)

The slope of f(x) is m = 3

The slope of a perpendicular line will have slope -1/m = -1/3

 

equation of line through (2,6) with slope -1/3

 

f(x) = (-1/3)x + b

Using (2,6) as (x, f(x)) find b

6 = (-1/3)(2) + b

 

b = 6 2/3 or 20/3

 

f(x) = (-1/3)x + 20/3