Answer:
C and D
Step-by-step explanation:
Let's actually find the line going through (3,6) and (1,-2).
As we go from (3, 6) to (1, -2), x decreases by 2 and y decreases by 8. Thus, the slope of this line is m = rise / run = -8/(-2), or m = 4.
Starting with the point-slope equation of a straight line, y - k = m(x - h), and substituting 4 for the slope, m, we get:
y - k = 4(x - h).
We could use either given point to be the general point (h, k).
If we use the point (3, 6), then y - 6 = 4(x - 3). This matches B. Thus, B is one form of the equation of the line going thru (3,6) and (1,-2), and so B is not the correct answer to the problem you have posted.
If we use the point (1, -2), then y + 2 = 4(x - 1). This matches A. Thus, A is one form of the equation of the line going thru (3,6) and (1,-2), and so A is not the correct answer to the problem you have posted.
Now take a look at Cy - 2 = 4(x + 1). This can be rewritten as
y = 4x + 4 + 2, or y = 4x + 6. Does (3, 6) satisfy this equation?
Is 6 = 4(3) + 6 true? NO. Thus, y = 4x + 6 (Equation C) is not an equation of the given line. Thus, C is a correct answer to the question you have posted.
Finally, let's look at D: y - 2 = 4(x + 1). Does the given point (1, -2) satisfy this equation? Is -2 -2 = 4(1 + 1) true? Is -4 = 8 true? NO. Thus, D is another correct answer to the question you have posted.
