The slope and a point on a line are given. Use this information to locate three additional...

The slope and a point on a line are given. Use this information to locate three additional points on the line. Answers may vary. [Hint:It is not necessary to Find the equation of the line. See Example 3.]

Slope 4; point (1, 2)

Graphing a Line Given a Point and a Slope

Draw a graph of the line that contains the point (3, 2) and has a slope of:

(a)  (b)

Solution

(a)  The fact that the slope is  means that for every horizontal movement (run) of 4 units to the right there will be a vertical movement (rise) of 3 units. Look at Figure. If we start at the given point (3, 2) and move 4 units to the right and 3 units up, we reach the point (7, 5). By drawing the line through this point and the point (3, 2), we have the graph.

Figure

(b) The fact that the slope is

means that for every horizontal movement of 5 units to the right there will be a corresponding vertical movement of –4 units (a downward movement). If we start at the given point (3, 2) and move 5 units to the right and then 4 units down, we arrive at the point (8, –2). By drawing the line through these points, we have the graph. See Figure.

Alternatively, we can set

Figure

so that for every horizontal movement of –5 units (a movement to the left) there will be a corresponding vertical movement of 4 units (upward). This approach brings us to the point (–2, 6), which is also on the graph shown in Figure.

Figure