Name _____________________________________________________ Date ____________ Color _________
Algebra I
Ms. Hahl
Introduction to Graphing Linear Equations
The Coordinate Plane:
A – The coordinate plane has 4 quadrants.
B – Each point in the coordinate plane has an x coordinate (the abscissa) and the y coordinate (the
ordinate). The point is stated as an ordered pair (x, y).
C – Horizontal Axis is the X-Axis. (y=0)
D – Vertical Axis is the Y-Axis. (x=0)
Directions: Plot the following points on the coordinate plane.
a)
b)
c)
d)
e)
f)
g)
h)
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Graphing Linear Equations
To graph a line (linear equation), we first want to make sure the equation is in slope intercept
form (y=mx+b). We will then use the slope and the y-intercept to graph the line.
Slope (m): Measures the steepness of a non-vertical line. It is sometimes refereed to as the
rise/run or change in y/change in x. It’s how fast and in what direction y changes compared to x.
y-intercept(b): The y-intercept is where a line passes through the y axis. It is always stated as
an ordered pair (x,y). The x coordinate is always zero. The y coordinate can be taken from the “b” in
y=mx+b.
Graphing The Linear Equation:
1) Find the slope:

=
=
2) Find the y-intercept:

3) Plot the y-intercept
4) Use slope to find the next point: Start at
 up 3 on the y-axis
 right 1 on the x-axis
Repeat:
5) To plot to the left side of the y-axis, go to y-int. and
do the opposite(Down 3 on the y, left 1 on the x)
Repeat:
6) Connect the dots.
Do Now: Graph the following linear equations.
1)
2)
2
3)
4)
5)
6)
7)
8)
3
Finding the Equation of a Linear Function
Finding the equation of a line in slope intercept form (y=mx + b)
Example: Find the equation in slope intercept form of the line formed by (3,8) and (-2, -7).
A. Find the slope (m):
B. Use m and one point to find b:
Have:
Special Slopes:
A. Zero Slope
* No change in Y
* Equation will be Y =
* Horizontal Line
B. No Slope (undefined slope)
* No change in X
* Equation will be X =
* Vertical Line
Practice Problems:
Find the equation in slope intercept form and then graph. (On some problems , the slope (m) is given, so
you only have to find the y-intercept (b).)
1)
2)
4
3)
5)
4)
6)
5
7)
8)
Directions: Find the equation of each line in slope intercept form and then graph:
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
6
Finding the Equation of a Parallel Line
Parallel Lines:
* Do not intersect
* Have same slopes
Example: Find for the given line, find a line that is parallel and
passes through the given point and then graph.
A) Given Line:
Given Point: (12, 9)
Parallel Line:
Do Now: For the given line, find a line that is parallel and passes through the given point and then
graph both lines..
Given Line:
Given Point:
1)
(6,1)
2)
7
Given Line:
Given Point:
3)
10)
Practice Problems:
Given Line:
1) (-5, 13) (3, -3)
3) (2,6)(-3,-19)
5) (2,-5) (-2, -5)
7) (8,-3) (-4,9)
9) (4,-3)(-6,-8)
a) Use the two points to find the equation of the line.
b) For the line found in part a, find a line that is parallel and passes through
the given point.
c) Graph both lines.
Parallel:
Given Line:
Parallel:
(4,-10)
2) (-6,0) (3,6)
(6,3)
(5,14)
4) (-4,3) (-8,6)
(-4, 10)
(8,-2)
6) (-9,-11)(6,9)
(-3,-9)
(-2, 14)
8) (3,6)(3,-6)
(11,-3)
(6,7)
10) (2,4)(-6,-12)
(-3,-5)
11) Find the equation of the line parallel to y = 3x – 2, passing through (-2, 1).
12) Find the equation of the line parallel to y = -¼ x + 2, passing through (-8, 7)
13) Find the equation of the line parallel to y = -5, passing through (2,7)
14) Find the equation of the line parallel to x= 8, passing through (4, -9)
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