Determine the equation of the line that goes through the points ( − 2 , 1 ) and (1,−1). The equation of the line is:

Answer 1

(-2, 1) and (1, -1) are two points with a line through them that has a slope = "rise over run" = difference in y coordinates divided by difference in x coordinates = (1--1)/(-2-1) = -2/3

a generic form of the slope is use two points as (x,y) and (-2,1) to get (y-1)/(x--2) = (y-1)/(x+2) = slope. set it = -2/3

(y-1)/(x+2) = -2/3

y-1 = (-2/3)x -4/3

y = -2x/3 -1/3 is the equation of the line in slope intercept form

check the answer by plugging in the points

for (-2,1) 1=-2(-2)/3 -1/3 = 4/3-1/3 = 1

for (1, -1) -1 = -2(1)/3 -1/3 = -2/3-1/3 = -1

y=-2x/3 -1/3 can also be rewritten as

3y =-2x -1

or

2x +3y + 1 = 0