In Problem, the slope and a point on a line are given. Use this information to locate thre...

In Problem, 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.]

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)

a)  The slope means that for every horizontal movement (run) of 4 units to the right, there will be a vertical movement (rise) of 3 units. Start at the given point (3, 2) and move 4 units to the right and 3 units up, arriving at the point (7, 5). Drawing the line through this point and the point (3, 2) gives the graph. See 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). Start at the given point (3, 2) and move 5 units to the right and then 4 units down, arriving at the point (8, − 2). Drawing the line through these points gives the graph. See Figure.

Figure 1

Alternatively, consider that

so 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

leads to the point (-2, 6), which is also on the graph of the line in Figure

Figure 2

Slope point (− 3, 2)