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

1 Answer
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