Let the given points be A(–1, 1) and B(2, –4).
We know that the equation of a line passing through the given points
(x1,y1) and (x2,y2) is given by

y−y1

x−x1

=

y2−y1

x2−x1

Here, x1 = – 1, y1 = 1, x2 = 2, y2 = – 4
So, the equation of a line passing through the given points is

y−1

x−(−1)

=

(−4−1)

2−(−1)

⇒

y−1

x+1

= −

5

3

⇒ 3 (y - 1) = - 5 (x + 1) ⇒ 5x + 3y + 2 = 0
Hence, the required equation is 5x + 3y + 2 = 0.