Find an equation of the line passing through the given points. (-1, 1) and (2, -4).

Solution:

To find an equation of a line two points are needed.

The given points are (-1, 1) and (2, -4).

The equation of the line is given by the (y - y₁) = m(x - x₁)

Where m = slope = (y₂ - y₁) / (x₂ - x₁)

= (-4 - 1)/(2 - (-1))

m = -5/3

Therefore the equation of the line is (y - 1) = (-5/3)(x - (-1))

(y - 1) = (-5/3)(x + 1)

3y - 3 = -5x - 5

5x + 3y = -2

5x + 3y + 2 = 0

Therefore, the equation of line passing through the given points. (-1, 1) and (2, -4) is 5x + 3y + 2 = 0.

Find an equation of the line passing through the given points. (-1, 1) and (2, -4).

Summary:

The equation of the line passing through the points (-1, 1) and (2, -4) is 5x + 3y + 2 = 0.