Write the equation of the line that passes through: (1,-4) and (5,3)?

The line through the two points (x₁,y₁) and (x₂,y₂) is given by (y₁-y₂)x + (x₂-x₁)y = (y₁x₂-x₁y₂) in General form, which can be manipulated to y = ((y₁-y₂)/(x₁-x₂))x + (x₁y₂-y₁x₂)/(x₁-x₂) in Slope Intercept Form.

This line is (3--4)x + (1-5)y = (3×1-5×-4) which simplifies to 7x - 4y = 23, or y = (7/4)x - 23/4

Graph: https://www.desmos.com/calculator/qc1amb9alq

Equation of the line :
[y - (-4)] / (x - 1)] = (y - 3) / (x - 5)
(y + 4) (x - 5) = (y - 3) (x - 1)
xy + 4x - 5y - 20 = xy - 3x - y + 3
7x - 4y - 23 = 0

(y + 4)/(x - 1) = (3 + 4)/(5 - 1)