Final answer:
The incorrect equation of the line going through the points (3,-6) and (1, 2) is Option C, y - 1 = -4(x - 2), which simplifies to a line that does not pass through both given points.
Step-by-step explanation:
The student's question is which of the following is not an equation of the line going through the points (3,-6) and (1, 2). To determine this, we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Applying the points given:
m = (2 - (-6)) / (1 - 3) = 8 / (-2) = -4.
Now, using point-slope form, which is y - y1 = m(x - x1), we can generate the correct equation of the line with any of the given points. Let's use point (3, -6).
y - (-6) = -4(x - 3)
Simplifying, we get:
y + 6 = -4(x - 3)
Option A is, therefore, the correct form. We need to find the one that does not represent the line. Now, let's inspect the other options to identify the incorrect one.
Option B, y = -4x + 6, is equivalent to y + 4x = 6, which is another linear form, and could be transformed into y + 6 = -4(x - 3) if we treated -4 as the slope and 6 as the y-intercept.
Option C, y - 1 = -4(x - 2), if you distribute the -4 you get y - 1 = -4x + 8 or y = -4x + 9, which is not the correct line as it does not pass through (3, -6).
Option D, y - 2 = -4(x - 1), simplifies to y = -4x + 6, which is the same as option B in a different form. So, it does represent the line.
Therefore, the equation that does not represent the line through the two points is Option C.