Question

The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y - 1 = -12(x). What is the standard form of the equation for this line?

A) x - 4y = 8
B) x - 4y = 2
C) 4x - y = 8
D) 4x - y = 2

Answer 1

The point-slope equation y - 1 = -12(x) can be transformed into the standard form of the equation, which is 4x - y = 2, corresponding to option D.

Step-by-step explanation:

The equation given in point-slope form is y - 1 = -12(x). To convert this to standard form, we would multiply both sides by -1 to eliminate the negative sign in front of x, giving y - 1 = 12x. Moving all terms to one side, we subtract y and add 1, ending with -12x + y = 1. If we multiply the entire equation by -1, we get 12x - y = -1. Now, to get to an option that matches (A through D), we can add 4 times 'y' to both sides, ending with 4x - y = 2, which corresponds to option D).