2. Graphing Points
We have graphed points on a line such as this.
a = 3½ 3½
1 2 3 4 5
But the truth is we do not live in a strictly linear world.
We live in a 3 dimensional world and write in a 2
dimensions. So how can we graph a point somewhere
above or below the line?
Lial: 9.4, 9.5 2
3. The Coordinate Grid
This is the reason why we have and use the coordinate grid.
We not only have the horizontal axis but now add a vertical
axis.
Because we now have a y
vertical and a horizontal
line we will label them for
easy identification.
The horizontal line will be
x & the vertical line will be y. (0,0)
x
The center of the grid is
the origin and will always
be (0,0), where the
x & y are 0.
Lial: 9.4, 9.5 3
4. The Coordinate Grid
From the center where both x & y
are zero the numbers will
sequentially increase to the right
and above and decrease to the left
and below.
The horizontal axis will have
positive numbers on the right and
negative numbers on the left.
The vertical axis will have positive
numbers above the horizontal and
negative numbers below.
Points to plot on the grid will be
given in a parenthesis.
Because alphabetically x comes
before y, the points are given as
(x,y).
Lial: 9.4, 9.5 4
5. The Coordinate Grid
The grid is divided into 4
distinct parts and they have
names. Quadrant II Quadrant I
(-,+) (+,+)
Starting from the upper
right and moving counter
clockwise we have
Quadrant I, II, III, & IV.
Quadrant III Quadrant IV
Points in Q I will be (+,+),
(-,-) (+,-)
Q II (-,+), QIII (-,-), & Q IV
(+,-).
Lial: 9.4, 9.5 5
6. Plotting Points on the
Coordinate Grid
When plotting points always (4,-2)
start at the origin.
Move left or right first as the x
value indicates. At the first (3,5)
move you will just hold the
spot. c (5,3)
From there move up or down
as the y value indicates.
(4,-2)
Once you have moved using
both numbers you will note
the point with a dot and a
label.
The point (3,5) will not be the
same as (5,3).
Lial: 9.4, 9.5 6
7. Plotting Points on the
Coordinate Grid
Plot the following points:
(2,3),
(-4,6),
(-4,6)
(0,-5),
(-1,-2) (2,3)
(-1,-2)
(0,-5)
Lial: 9.4, 9.5 7
8. Graphing Linear Equations
Using the knowledge of graphing x y
points we can further use the -2 Put each value in the
coordinate grid to graph linear original equation and
equations. -1
0 solve for the y. This will
They are named linear because if we do 1 go in the chart next to
all our work correct the points on the 2 the corresponding
graph will form a straight line. value.
In linear equations there will usually be
both an x & y. -2 + y = 6 -1 + y = 6
Using this example: +2 +2 +1 +1
x+y=6 y=8 y=7
We can find points that will lie on this
line. We will begin with a chart. 1+y=6
0+y=6
For the x-coordinates we will always use y=6 -1 -1
-2,-1,0,1,2. Fill these numbers in the y=5
chart.
2+y=6
-2 -2
y=4
Lial: 9.4, 9.5 8
9. Graphing Linear Equations
x+y=6
x y (-2,8)
(-1,7)
(0,6) (1,5)
-2 8
(2,4)
-1 7
0 6
1 5
2 4
--The line looks slightly off
because I was unable to place
the dots exactly in place.
Lial: 9.4, 9.5 9
10. Graphing Linear Equations
When the linear equation is given in slope intercept form you will choose the x
points in a way that will make calculations easier. For example:
y = ⅓x + 4
If we pick x = -2,-1,0,1,& 2, our answers for y will be fractions.
y = ⅓(-2) + 4
y = -2/3 + 4
y = -2/3 + 12/3
y = 10/3
This can be hard to calculate as well as graph.
Instead lets look at what would happen to the denominator if I used -3.
y = ⅓ (-3) + 4
y = -1 + 4
y=3
Why did this work out better?
The -3 would divide evenly into the denominator of one third.
Besides three and negative three what would be a good choice?
Lial: 9.4, 9.5 10
11. Slope
The slope of a line has to do
with the direction of the line
when x is positive.
Consider the red line. Is the line
increasing or decreasing as you
move to the right?
Since it is decreasing the line
has a negative slope.
Consider the blue line. Is the
line increasing or decreasing as
you move to the right?
Since it is increasing the line has
a positive slope.
Lial: 9.4, 9.5 11
