Question

Brian drew a line through points A(-1,-4) and B(2,5). He drew another line through points C(3,-7) and D(5,-1). The slopes of the two lines are_____ . The slope of vector AB is _____

(A) The slopes are different; the slope of vector AB is undefined.
(B) The slopes are different; the slope of vector AB is 3.
(C) The slopes are equal; the slope of vector AB is 3.
(D) The slopes are equal; the slope of vector AB is undefined.

Answer 1

The slopes of the lines AB and CD are both 3, so they are equal, and the slope of vector AB is 3, corresponding to answer option (C).

Step-by-step explanation:

To find the slopes of the lines through points A(-1, -4), B(2, 5), C(3, -7), and D(5, -1), we need to use the slope formula m = (y2 - y1) / (x2 - x1). For line AB, this gives us m = (5 - (-4)) / (2 - (-1)) = 9 / 3 = 3. For line CD, the slope would be m = (-1 - (-7)) / (5 - 3) = 6 / 2 = 3.

Since both slopes are equal, they are not different and the slopes of the lines AB and CD are identical. Thus the slopes are equal, and the slope of vector AB is 3, making the correct answer (C).