Download Graphing Lines

Plotting Points
To graph a point, we need two axes, the x-axis and the y-axis.
The y-axis is the one that points to the sky.
The x-axis runs horizontally, and the y-axis runs vertically.
When plotting an ordered pair of numbers, the first number corresponds to a direction along the
x-axis and the second number corresponds to a direction parallel to the y-axis.
One way to remember the order for the ordered pair is x comes before y, just like in the
dictionary.
To plot a point, start at the origin, where the x-axis and y-axis cross.
Move to the right if the first number in the ordered pair is positive, left if it is negative. From
that location, move up if the second number of the ordered pair is positive, down if it is negative.
+y
•
A
A: (2, 5)
B: ( -1, 3)
+x
C: (4, -2)
D: (0, -3)
E: (5, 0)
There are 4 quadrants in the rectangular coordinate system.
Quadrant I is the upper right section between the x-axis and the y-axis. The signs are: (+, +)
Quadrant II is the upper left section between the x-axis and the y-axis. The signs are: ( -, +)
Quadrant III is the lower left section between the x-axis and the y-axis. The signs are: ( -, -)
Quadrant IV is the lower right section between the x-axis and the y-axis. The signs are: (+, -)
Ordered pairs are always written with x as the first coordinate (abscissa) and y as the second
coordinate (ordinate).
Is (2, -3) a solution of y = x + 5?
Find the ordered-pair solution of y = ½ x + 3 that corresponds to x = 4.
When graphing by plotting points, you choose values for x and find the corresponding value for y.
Use an x-y table, and find at least 5 points, you must plot at least 4 points for full credit.
My favorite numbers to use for x are: -2, -1, 0, 1, 2. Unless the coefficient of x is a fraction, then
I use multiples of the denominator.
Graph by plotting points.
y = 3x – 1
x|y .
y = 3( ) – 1
y = 3( ) – 1
y = 3( ) – 1
y = 3( ) – 1
y = 3( ) – 1
Graph by plotting points.
y=½x+3
x|y .
Note: If the graph crosses the x-axis, it is called an x-intercept and the y value is zero.
If the graph crosses the y-axis, it is called an y-intercept and the x value is zero.
Intercepts: where the graph crosses the x-axis and/or y-axis.
Let x = 0, then find the value for y.
Let y = 0, then find the value for x.
Unlike when graphing by plotting points, graphing using intercepts requires that you plot 2 and
only 2 points. One on each axis.
Graph the linear equation by locating the y-intercept and the x-intercept.
Recall, intercepts are where the graph crosses the axes.
y = 0 for an x-intercept and x = 0 for a y-intercept.
3x – 7y = -21
y-intercept:
3 (0) – 7y = -21
– 7y = -21
y= 3
(0, 3)
x-intercept:
3x – 7(0) = -21
3x
= -21
x = -7
(-7, 0)
Graph by using x- and y-intercepts.
3x – y = 3
x
y .
Graph using Intercepts.
x+y=3
x
y .
Graph by using the Slope-Intercept form.
The equation must be solved for y.
y = mx + b
Note: m = slope
b = y-intercept
Graph by slope-intercept form.
y = 3/2 x + 1
Begin on the y-axis as indicated
by the constant (# by itself)
From that point,
go up and over
or
go down and over
Graph using slope-intercept form.
y=½ x – 4
y = -3 x + 5
Graph using slope-intercept form.
y = 2x – 3
y = -3/4 x + 2
Graph using slope-intercept form.
y = 4/5 x
y = -2 x – 1
Graph by slope-intercept form.
Remember to solve for y.
-x + y = 4
Graph by slope-intercept form.
2x + 3y = 9
Find the slope and the y-intercept. Graph the line.
y=3
x = -2
x=4
y = -1
Graph using Slope-Intercept form
x – 2y = -6
Graph by slope-intercept form.
2x – 5y = 8