Question

find the equation of the straight line passing through the points -1,1 and 2,-4

Answer 1

The equation of the line is
5x+3y+2=0 is the equation of a straight line

Answer 2

let slope of line passing through (-1, 1) and (2, -4) is m .
we know,
if two points :
$(x_1,y_1)\:\:and\:\:(x_2,y_2)$
are given then,
$slope (m) = \frac{y_2-y_1}{x_2-x_1}\\\\so,slope\:of\:line(m)=\frac{-4-1}{2+1}\\=\frac{-5}{3}$

now, equation of line is
(y - y₁ ) = m(x - x₁) , here Let (x₁ , y₁ ) = (-1,1) [ you can also let (x₁ , y₁ ) = (2, -4) . because result will be same ]
then,
(y - 1) = (-5/3)(x + 1)
3(y -1) + 5(x + 1) = 0
3y - 3 + 5x + 5 = 0
5x + 3y + 2 = 0

hence, equation of line : 5x + 3y +2 = 0