Using Slopes to Graph Lines
We have graphed a line by making a table of at least two ordered pairs and
plotting the ordered pairs on a Cartesian coordinate system.
If we are given only one point on a line, we can graph the line if we also
know its slope.
Procedure â€”
To Graph a Line Using a Point and the Slope
Step 1 Plot any point on the line.
Step 2 From this point, rise in the ydirection the number of units in
the numerator of the slope.
Step 3 Then run in the xdirection the number of units in the
denominator of the slope. Plot a point at this location.
Step 4 Draw a line through the two points.
Note:
We â€œriseâ€ in the ydirection
and â€œrunâ€ in the xdirection.
positive rise: move up
negative rise: move down
positive run: move right
negative run: move left
Example 1
Graph the line that passes through the point (4, 3) with slope
Solution
Step 1 Plot any point on the line.
Plot the given point (4, 3).
Step 2 From this point, rise in the ydirection the number of units in the
numerator of the slope.
The slope is
We can write this as
. Thus, the rise is
2.
From (4, 3), move down 2 units to (4, 5).
Step 3 Then run in the xdirection the number of units in the
denominator of the slope. Plot a point at this location.
We wrote the slope as
, so the run is 3.
From (4, 5) move 3 units to the right to (7, 5).
Place a dot at (7, 5).
Step 4 Draw a line through the two points.
Draw the line through (4, 3) and (7, 5).
Note:
We could also write the slope,
, as
. Then, the rise is
2 and the run is 3.
Using that rise and run, we end up at
(1, 1). That point is also on the line.
