To determine the point-slope form of the line with a given slope of -12 that passes through the point (5, 3), we need to use the point-slope formula.
The point-slope form of a linear equation is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.
Here, the point given is (5, 3), so [tex]\((x_1, y_1) = (5, 3)\)[/tex], and the slope [tex]\(m\)[/tex] is -12. Plugging these values into the point-slope formula gives us:
[tex]\[ y - 3 = -12(x - 5) \][/tex]
Thus, the equation of the line in point-slope form is:
[tex]\[ y - 3 = -12(x - 5) \][/tex]
This matches option D.
Therefore, the correct choice is:
D. [tex]\(y - 3 = -12(x - 5)\)[/tex]
