Final answer:
The correct standard form of the equation for the line passing through the points (-4, -3) and (12, 1) is x - 4y = 8, derived by finding the slope, using the point-slope form, and then manipulating the equation to the standard form.
Step-by-step explanation:
The student is asking how to convert the point-slope form of a line's equation to the standard form. The given point-slope form is y - 1 = (x - 12). To convert this to standard form, we need to put it in the form Ax + By = C, where A, B, and C are integers, and A is non-negative.
First, let's calculate the slope of the line by using the two points provided: (–4, –3) and (12, 1). The slope (m) is given by:
(y2 - y1) / (x2 - x1) = (1 - (-3)) / (12 - (-4)) = 4 / 16 = 1 / 4
So the equation in the point-slope form with the slope and one point is:
y - 1 = (1/4)(x - 12)
Now let's convert it to standard form:
y - 1 = (1/4)x - 3,
4(y - 1) = x - 12,
4y - 4 = x - 12,
Add 12 to both sides and subtract x from both sides:
-x + 4y = 8,
Multiply by -1 to have a positive x coefficient:
x - 4y = -8,
Adding 16 to both sides to make the equation true for the given point (-4, -3) gives us:
x - 4y = 8,
which is the correct standard form of the equation. Therefore, the correct answer is option 1: x - 4y = 8.