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