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

##### 1 Answer

#### 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

#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

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

Now you need to find its

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

Pick one of the two points and use its coordinates to replace

#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#