How do you write a general linear equation for the line that crosses (-2,1) and (2,-2)?

1 Answer
Stefan V.
Sep 1, 2015

#y = -3/4x - 1/2#

Explanation:

In order to determine the equation of a line given two points that are on that line, you need to deterime two things

  • the line's slope;
  • the line's y-intercept.

For a line that passes through two points #(x_1, y_1)# and #(x_2, y_2)#, the slope of the line is defined as

#color(blue)(m = (y_2 - y_1)/(x_2 - x_1))#

Use the coordinates of the two points given to you to determine the slope of the line - it doesn't matter which point you take to be #(x_1, y_1)# and which you take #(x_2, y_2)#.

#m = (-2 - 1)/(2 - (-2)) = ((-3))/4 = -3/4#

Now you need to find its #y#-intercept. The slope-intercept form for a line is given by the equation

#color(blue)(y = mx + b)" "#, where

#m# - the slope of the line;
#b# - the #y#-intercept.

Pick one of the two points and use its coordinates to replace #x# and #y# in the slope-intercept form equation, and use the calculated value of #m# to get the #y#-intercept

#1 = -3/4 * (-2) + b#

#1 = 3/2 + b implies b = 1 - 3/2 = -1/2#

The slope-intercept equation of the line is

#y = -3/4x - 1/2#

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