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)
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)
3) 4)
5)6)
7) 8)
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 SlopeB. No Slope (undefined slope)
* No change in Y * No change in X
* Equation will be Y = * Equation will be X =
* Horizontal Line * 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)
3) 4)
5) 6)
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)
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)
Given Line: Given Point:
3)
10)
Practice Problems: 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.
Given Line:Parallel:Given Line:Parallel:
1) (-5, 13) (3, -3)(4,-10)2) (-6,0) (3,6)(6,3)
3) (2,6)(-3,-19)(5,14)4) (-4,3) (-8,6)(-4, 10)
5) (2,-5) (-2, -5)(8,-2)6) (-9,-11)(6,9)(-3,-9)
7) (8,-3) (-4,9)(-2, 14)8) (3,6)(3,-6)(11,-3)
9) (4,-3)(-6,-8)(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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