Second Term Lesson Note for Week Five
Class : JSS 2
Subject : Mathematics
Topic : Graphs of Linear Equation
Duration : 80 Minutes
Period : Double Period
Reference Book :
Essential Mathematics for Junior Secondary School, JSS 2.
Lagos State Unified schemes of work for Junior Secondary Schools, JSS 1 – 3.
Online Resources
Instructional Material : Chart showing Graphs of Equations
Learning Objectives : By the end of the lesson learners will be able to :
Content :
GRAPH OF LINEAR EQUATION
There are several ways to graph a straight line given its equation.
Let’s quickly refresh our memories on equations of straight lines:
Slope Intercept Form
Point Slope Form
Horizontal Lines
Vertical Lines
when stated in “y=” form, it quickly gives the slope, m, and where the
line crosses the y-axis, b, called the y-intercept.
when graphing, put this equation into “y = ” form to easily read graphing information.
y = 3 (or any number)
horizontal lines have a slope of zero – they have “run”, but no “rise” — all of the y values are 3.
x = -2 (or any number)
vertical lines have no slope (it does not exist) – they have “rise”, but no “run” –all of the x values are -2.
Graphing Tidbits:
If a point lies on a line, its coordinates make the equation true.
(2,1) in on the
line y = 2x – 3
because 1 = 2(2) – 3
Before graphing a line, be sure that your equation starts with “y=”.
To graph 6x + 2y = 8
rewrite the equation:
2y = -6x +8
y = -3x + 4
Now graph the line using either slope intercept method or chart method.
The x-coordinate may be called the abscissa.
The y-coordinate may be called the ordinate.
Equations and Graphing
Topic Index | Algebra Index | Regents Exam Prep Center
There are several ways to graph a straight line given its equation.
Let’s quickly refresh our memories on equations of straight lines:
Slope Intercept Form
Point Slope Form
Horizontal Lines
Vertical Lines
when stated in “y=” form, it quickly gives the slope, m, and where the
line crosses the y-axis, b, called the y-intercept.
when graphing, put this equation into “y = ” form to easily read graphing information.
y = 3 (or any number)
horizontal lines have a slope of zero – they have “run”, but no “rise” — all of the y values are 3.
x = -2 (or any number)
vertical lines have no slope (it does not exist) – they have “rise”, but no “run” –all of the x values are -2.
Graphing Tidbits:
If a point lies on a line, its coordinates make the equation true.
(2,1) in on the
line y = 2x – 3
because 1 = 2(2) – 3
Before graphing a line, be sure that your equation starts with “y=”.
To graph 6x + 2y = 8
rewrite the equation:
2y = -6x +8
y = -3x + 4
Now graph the line using either slope intercept method or chart method.
The x-coordinate may be called the abscissa.
The y-coordinate may be called the ordinate.
Methods of Graphing a Line
Using y = mx + b
with rise/run
Using a Chart –
Plotting Points
Graph 2y = 6x + 4
1. Put your equation in “y=” form.
y = 3x + 2
2. The number in front of x is the slope.
(If necessary, place this number over 1 to
form a fraction for your rise/run.)
slope = 3/1
3. The “b” value is where the line crosses the
y-axis. Be sure to check the sign of this
number. b = 2
4. Plot the b value on the y-axis.
see graph below
5. Standing at this point, use your rise and run
values to plot your second point.
(If rise is positive, move up. If rise is negative,
move down.)
(If run is positive, move right. If run is
negative, move left.)
6. Connect the two points to form the line.
Graph 2y = 6x + 4
X
Y
-3
-2
-1
0
1
2
3
Create a chart to hold x and y values from your line. For lines, the x-values usually range from -3 to +3, but may be any values you wish.
While charts often contain more than 2 entries, only two entries are needed to determine a straight line. A third point should be used to “check” that an error was not made while computing the first two points.
X
Y
-3
-7
-2
-4
-1
-1
0
2
1
5
2
8
3
11
Substitute the x-values into the equation to determine the y-values. Putting the equation in “y=” form first will make the substitution easier.
y = 3x + 2
Now start substituting. For example, substitute x = -3:
y = 3 (-3) +2 = -9 + 2 = -7
Plot the (x,y) coordinates to graph the line.
Bottom of Form
How Do You Graph a Linear Equation by Making a Table?
Note:
Graphing a function? It would be really helpful if you had a table of values that fit your equation. You could plot those values on a coordinate plane and connect the point to make your graph. See it all in this tutorial!
Graphing in the Coordinate Plane
How Do You Plot Points in the Coordinate Plane?
Knowing how to plot ordered pairs is an essential part of graphing functions. In this tutorial, you’ll see how to take an ordered pair and plot it on the coordinate plane. Take a look!
What is an Ordered Pair?
Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!
What is the Origin?
The coordinate plane has two axes: the horizontal and vertical axes. These two axes intersect one another at a point called the origin. Learn about the ordered pair that indicates the origin and its location in the coordinate plane by watching this tutorial!
What is the X-Coordinate?
Ordered pairs are a crucial part of graphing, but you need to know how
Identifying Linear Equations
What’s Standard Form of a Linear Equation?
A linear equation can be written in many different forms, and each of them is quite useful! One of these is standard form. Watch this tutorial and learn the standard form for a linear equation!
Further Exploration
Working With Graphs
How Do You Check if a Point is on a Line If You Have a Graph?
Wonder if a point is part of a line? You could take that equation and graph it. Then use the graph to get your answer! Watch how in this tutorial.
Finding Slopes