The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
From the information given,
the given points are (- 2, 2) and (3, - 3). From the points,
x1 = - 2, y1 = 2
x2 = 3, y2 = - 3
m = (- 3 - 2)/(3 - - 2) = - 5/(3 + 2) = - 5/5 = - 1
We would find the y intercept, c by substituting m = - 1, x = - 2 and y = 2 into the slope intercept equation. We have
2 = - 1 * - 2 + c
2 = 2 + c
c = 2 - 2 = 0
By substituting m = - 1 and c = 0 into the slope intercept equation, the equation of the line is
y = - x