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On a coordinate plane, a line goes through (negative 4, 4) and (4, negative 2). A point is at (6, 0). What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6? y = –Three-fourthsx + 8 y = –Three-fourthsx + 6 y = Four-thirdsx – 8 y = Four-thirdsx – 6

2 Answers

6 votes

Answer:

in other words the answer is CCCCCCCCCCCCCCCCCCCCCCCC

User Nik FP
by
4.6k points
4 votes

y = Four-thirds x – 8

Explanation:

Step 1:

First step is to find the slope of the line joining the 2 given points

(negative 4, 4) and (4, negative 2).

Formula for finding the slope of the line joining 2 given points is

Slope m = (change in y)/(change in x)

Using the above formula , the slope of the line joining the 2 given points

is m = (-2-4)/(4-(-4)) = -6/8 =-3/4

Step 2 :

Find the slope of the line perpendicular to the line joining the 2 given

points

Slopes of 2 perpendicular lines are negative reciprocals of each other

, i.e if m1 and m2 are slopes of 2 lines then m1*m2 = -1, if the lines are

perpendicular to each other.

Hence the slope of the line perpendicular to the line joining the above 2

given points is

m1*m2 = -1 => (-3/4)*m2 = -1 => m2 = 4/3

Step 3 :

Find the equation of the line with slope 4/3 and has an x- intercept of 6

X intercept of 6 means the line passes through the point (6,0)

Equation of a line passing through a given point and having a slope

of m is (y - y1) = m(x-x1).

Substituting slope as m= 4/3 and point (x1,y1) as (6,0) in the above

equation,

(y-0) = (4/3)(x-6)

=> y = (4/3)x - (4/3)*6

=> y = (4/3)x - 8

Hence the required answer is y = (4/3)x - 8

User Paul Androschuk
by
4.4k points