To write the equation in standard form, we need to rearrange the equation so that the x and y terms are on the same side, and the constant term is on the other side.
1) Start with the equation y = 3x + 13.
2) To remove the fractions, we can multiply the entire equation by 3 (the coefficient of x).
3(y) = 3(3x + 13)
Simplifying, we get 3y = 9x + 39.
3) Next, we want to rearrange the equation to get it in the form Ax + By = C, where A, B, and C are integers.
-9x + 3y = 39.
4) Multiply the entire equation by -1 to make the coefficient of x positive.
9x - 3y = -39.
5) Since the standard form requires that the coefficient of x is positive, we can divide the entire equation by -3 to make it positive.
-3x + y = -13.
Therefore, the equation of the line in standard form that passes through the point (4, -1) and has a slope of 3 is -3x + y = -13.