B

Step 1: Slope of the line passing through the points (x₁, y₁) and (x₂, y₂) is y2-y1x2-x1.

Step 2: [Substitute the values of x₁ = 3, y₁ = - 2, x₂ = 7 and y₂ = - 5.]Slope of the line, m = - 5 - (- 2)7-3

Step 3: [Simplify the fraction.]m = - 34

Step 4: The equation of the line passing through the point (x₁, y₁) with slope m in point-slope form is y - y₁ = m(x - x₁).

Step 5: [Substitute x₁ = 3, y₁ = - 2 and m = - 34.] y - (- 2) = - 34(x - 3)

Step 6: [Simplify the equation.]y + 2 = - 34(x - 3)

Step 7: The equation of the line in point-slope form is y + 2 = - 34(x - 3) .