The document reviews methods for graphing linear equations, highlighting techniques such as using two points, x- and y-intercepts, and slope with a point. It includes illustrative examples and exercises for practice on each method to enhance understanding of linear equations. The importance of graphing in real-life situations is also emphasized, with additional activities for summarizing graphing steps.

1. Graph of Linear
Equations

2. Review
How to determine the
slope of a line?

3. How can you describe
linear equations by
graphing?

4. Graph of Linear
Equations

5. Plot on a graph the points
(2, 3) and (-1 ,-1)

6. Learning Competency
Graph a linear equation given (a) any two
points; (b) the x – and y– intercepts; (c) the
slope and a point on the line. M8AL-If-2
Objectives:
1. Solve for the value of y in behalf of x
2. Graph the equation using any two points

7. Graph of Linear Equations
Linear function can be described by its
equation, either in the form y = mx + b or
Ax + By = C. A linear equation can also be
described by its graph. Graphing linear
equations can be done using any of the four
methods:
1. Using any two points on the line
2. Using x- and y-intercepts
3. Using the slope and a point

8. Using Two Points on the line
One method of graphing a linear
equation is using two points. In
Geometry, you learned that two points
determine a line. Since the graph of the
linear equation is a line, thus two points
are enough to draw a graph of a linear
equation.

9. Illustrative Example
Graph the function y = 2x + 1.
You may assign any two values for x, say 0 and 1.
By substitution,
y = 2x + 1 y = 2x + 1
y = 2(0) + 1 y = 2(1) + 1
y = 0 + 1 y = 2 + 1
y = 1 y = 3
If x = 0, then y = 1. Furthermore, if x = 1, then y = 3. So, the
ordered pairs are (0, 1) and (1, 3). This means that the line
passes through these points.

10. After finding
the ordered
pairs of the two
points, plot and
connect them.
Your output is
the graph of the
linear equation.

11. Exercise 8
Graph each linear equation that passes
through the given pair of points.
1. (1, 2) and (3, 4)
2. (5, 6) and (0, 11)
3. (-2, ) and (, -)
4. (-, -) and (, )

12. Answers
1. 3.
2. 4.

13. Using x-Intercept and y-Intercept
Secondly, the linear equation can be
graphed by using x-intercept a and y-
intercept b. The x- and y-intercepts of the
line could represent two points, which
are (a, 0) and (0, b). Thus, the intercepts
are enough to graph the linear equation.

14. Illustrative Example
To graph the equation y = 2x + 1 using this method, you need
to solve the x-intercept by letting y = 0 and the y-intercept by
letting x = 0.
Letting y = 0, the equation y = 2x + 1 becomes
0 = 2x + 1 Substitution
-2x = 1 Addition Property of Equality
x = -12 Multiplication Property of Equality
Letting x = 0, y = 2x + 1 becomes
y = 2(0) + 1 Substitution
y = 0 + 1 Simplification
y = 1 Simplification
The x-intercept a is -12 while the y-intercept b is 1.

15. Now, plot the x-
and y-
intercepts, then
connect them.
The x-intercept is the abscissa of the coordinates of the point in
which the graph intersects the x-axis. However, the y-intercept is
the ordinate of the coordinates of the point in which the graph
intersects the y-axis.

16. Exercise 9
Graph each linear equation whose x-
intercept a and y-intercept b are given
below.
1. a = 2 and b = 1
2. a = 4 and b = -1
3. a = -2 and b = -7
4. a = and b = -2

17. Answers
1. 3.
2. 4.

18. Using Slope and a Point
The third method in graphing linear
equation is by using the slope and one
point. This can be done by plotting first
the given point, then finding the other
point using the slope.

19. The linear equation y =
2x + 1 has a slope of 2
and a point (-1, -1). To
find a point from this
equation, we may
assign any value for x in
the given equation. Let’s
say, x = -1. The value of y
could be computed in
the following manner:

20. Exercise 11
Graph the following equations given
slope m and a point.
1. m = 3 and (0, -6)
2. m = -2 and (2, 4)
3. m = and (0, 4)
4. m = and (2, -3)

21. Answers
1. 2.

22. Answers
3. 4.

23. Group Board Work Contest
The class will be divided into 4
groups. In every problem given, 2
representative of the group can go to the
board and write the answer/solutions on
the board. The first group to answer
correctly will receive the point.

24. How important
is graphing in
real life
situations?

25. Generalization
The graph of a linear equation can be
drawn in the coordinate plane using
any two points, the x- and y- intercepts
of the line, slope and y-intercept and
using slope and one point. Graphing is
a clear representation of data which
could easily be understood.

26. Additional Activity: Write the Steps
Description: This
activity will enable you
to summarize the
methods of graphing a
linear equation.
Direction: Fill in the
diagram below by
writing the steps in
graphing a linear
equation using 4
different methods.

27. Thank you
for your
cooperation!
Janette M. Basco, SST-I
San Vicente National High School