We want the equation of the line through the points (1, -4) and (-2, 5)
So we start by finding the slope of the segment that joins those two points using the formula for slope:
slope = (y2 - y1) / (x2 - x1)
slope = (5 - -4) / (-2 - 1) = 9 / (-3) = -3
Then the slope is -3
Now we use the general slope-intercept form of a line:
y = m x + b
with m = -3
y = -3 x + b
and request one of the points to be on the line in order to determine "b"
-4 = -3 (1) + b
- 4 = -3 + b
add 3 to both sides to isolate b on the right
- 4 + 3 = b
then b = -1
Then the equation of the line is:
y = -3 x - 1