What is the equation of the line between #(-20,2)# and #(-3,8)#?

Question

Eli Assouline · Accepted Answer

#6x-17y+154=0# Equation of a line joining two points #(x_1,y_1)# and #(x_2,y_2)# is #(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)# Hence equation of line joining #(-20,2)# and #(-3,8)# is #(y-2)/(8-2)=(x-(-20))/(-3-(-20))# or #(y-2)/6=(x+20)/17# or #17y-34=6x+120# or #6x-17y+154=0#

Hazel Anglin · Answer

undefined The equation of the line passing through the points (-20, 2) and (-3, 8) can be found using the point-slope formula:

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

where $ (x_1, y_1) $ is one of the given points and $ m $ is the slope of the line.

First, find the slope:

$ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $

$ m = \frac{{8 - 2}}{{-3 - (-20)}} $

$ m = \frac{{6}}{{17}} $

Next, choose one of the given points. Let's choose (-20, 2):

$ x_1 = -20 $ and $ y_1 = 2 $

Substitute the slope and the point into the point-slope formula:

$ y - 2 = \frac{{6}}{{17}}(x - (-20)) $

$ y - 2 = \frac{{6}}{{17}}(x + 20) $

$ y - 2 = \frac{{6}}{{17}}x + \frac{{120}}{{17}} $

$ y = \frac{{6}}{{17}}x + \frac{{120}}{{17}} + 2 $

$ y = \frac{{6}}{{17}}x + \frac{{120}}{{17}} + \frac{{34}}{{17}} $

$ y = \frac{{6}}{{17}}x + \frac{{154}}{{17}} $

So, the equation of the line passing through the points (-20, 2) and (-3, 8) is $ y = \frac{{6}}{{17}}x + \frac{{154}}{{17}} $.