Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2,4) and D(1,7).

Explanation:-

The problem asks us to find the slope of the line passing through two given points, A(4, 8) and B(5, 5). The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:

slope = (y2 – y1) / (x2 – x1)

Using this formula, we can find the slope of the line passing through A and B as follows:

slope of AB = (5 – 8) / (5 – 4) = -3 / 1 = -3

Similarly, we are given two more points C(2, 4) and D(1, 7), and we need to find the slope of the line passing through them:

slope of CD = (7 – 4) / (1 – 2) = 3 / (-1) = -3

We can see that the slopes of both lines are equal and negative. Two lines are parallel if and only if their slopes are equal. In this case, the slopes of the two lines are equal and negative. Therefore, the two lines are parallel.