Compute the slopes of the line segments determined by the given pairs of points. In each case, tell whether the segment is vertical, is horizontal, slopes upward to the right, or slopes downward to the right. Complete parts (a) through (c) below. (a) P(4, 3), Q(8, 19) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 0 of 1 A. The slope of the line segment determined by the given points is 4 . The slope of the line segment determined by the given points is undefined. Determine if the segment is vertical, is horizontal, slopes upward to the right, or slopes downward to the right. Choose the correct answer below. A. The segment slopes upward to the right. B. The segment slopes downward to the right. C. The segment is vertical. D. The segment is horizontal. (b) R(4, 7), S(4, -8) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line segment determined by the given points is \( \square \). B. The slope of the line segment determined by the given points is undefined. ( 10 .
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To compute the slope of a line segment given two points, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Now, let's solve the problems: (a) For the points P(4, 3) and Q(8, 19): \[ m = \frac{19 - 3}{8 - 4} = \frac{16}{4} = 4 \] The slope is 4, which is positive! Since it's positive, the segment slopes upward to the right. So, the answer is: A. The slope of the line segment determined by the given points is 4. The segment slopes upward to the right. (b) For the points R(4, 7) and S(4, -8): \[ m = \frac{-8 - 7}{4 - 4} = \frac{-15}{0} \] Since division by zero is undefined, the slope of the segment is undefined. Given that both points have the same x-coordinate, the segment is vertical. So, the answer is: B. The slope of the line segment determined by the given points is undefined. The segment is vertical.
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