Question

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

Short answer

A straight, horizontal line passing through points \(A(2,3)\) and \(B(-1,3)\) is the graph required. The slope, \(m\), of this line \(L\) is 0.

Step-by-step solution

Plot points \(A\) and \(B\)

Position point \(A\) at coordinates (2,3) and point \(B\) at (-1,3). Both points are easy to locate since they are located at the same height (y-axis value = 3) but differ in their displacement from the origin on the x-axis.

Compute the slope of \(L\)

The slope of a line, represented by \(m\), is calculated using the formula: \(m = \frac{y2 - y1}{x2 - x1}\). Here, \(y2\) and \(y1\) represent the y-coordinates of points \(A\) and \(B\), and \(x2\) and \(x1\) represent the x-coordinates of the same points. Thus, \(m = \frac{3 - 3}{-1 - 2}\) simplifies to \(m = 0\). This implies that the line \(L\) is horizontal.

Graph the line \(L\)

Line \(L\) can be drawn as a straight line passing through points \(A\) and \(B\). As calculated before, the line is horizontal because the slope is zero. Thus, the line \(L\) will be parallel to the x-axis, passing through the points \(A\) and \(B\) at y=3.