Given two points (6, 1) and (5, 4), what we can solve first is the slope of the line using the equation

Let x1 = 6, y1 = 1, x2 = 5, and y2 = 4. Solve for m, we get

The point-slope form of a line is written in the equation as

Substitute the values of y1, m, and x1 on the equation above, we get

Simplifying the equation above, we arrive to the slope-intercept form of the equation

To write this in standard form, let's put x and y on one side of the equation. We have

Therefore, the standard form of the line that passes through (6, 1) and (5, 4) is 3x + y = 19.