Question

In Exercises \(5-8,\) let \(L\) be the line determined by points \(A\) and \(B .\) \(\begin{array}{ll}{\text { (a) Plot } A \text { and } B .} & {\text { (b) Find the slope of } L} \\ {\text { (c) Draw the graph of } L .}\end{array}\) $$A(1,2), \quad B(1,-3)$$

Short answer

Line L, passing through points A(1,2) and B(1, -3), is a vertical line. Its slope is undefined.

Step-by-step solution

Drawing Points A and B

In the first part of this exercise, plot the points A(1, 2) and B(1, -3) on a graph. Both points have the same x coordinate and different y coordinates.

Calculating the Slope

The slope of a line is given by the formula (y2 - y1)/(x2 - x1) where (x1, y1) and (x2, y2) are coordinates of two points on the line. In this case, however, as x1 equals x2, the formula will lead to a division by zero, which is undefined. Therefore, the line passing through these points is a vertical line and its slope will be undefined.

Drawing the Graph of the Line

Based on the identified coordinates, draw a straight vertical line passing through the points A and B. This line represents the line L in the xy plane.