8

MATHEMATICS
FIRST QUARTER – MODULE 12
Describing the Graph of a
Linear Equation in Terms of
Its Intercepts and Slopes

Laboratory High School |

What I Need to Know

 This module was designed and written with you in mind. It is here to help
you master the descriptions of the graph of a linear equation in terms of its
intercepts and slope. The scope of this module permits it to be used in many
different learning situations. The language used recognizes the diverse vocabulary
level of students. The lessons are arranged to follow the standard sequence of the
course. But the order in which you read them can be changed to correspond with
the textbook you are now using.

In this module, you will be able to:

• describe the graph of a linear equation in terms of its intercepts and

slope. M8AL-If-3

Specifically, you are expected to:

1. graph linear equations in two variables using its intercepts and slope;
and
2. describe the graph linear equations in two variables using its intercepts
and slope.
 Describing the Graph of a
Lesso Linear Equation in Terms
of
n 1 Its Intercepts and Slope
Previously, you have learned that a Linear Equation in two variables can be
graph using various methods such as (a) using two points; (b) using x- and y-
intercepts; and (c) using slope and one point. Let us see if you can still recall your
previous lessons through the next activity.

What’s In

Before we proceed to our lesson proper, lest us review first what we have discussed
in the previous module.

Activity 1: You graph me!

Direction: Complete the table of values and sketch the graph of each equation by
plotting first the points on a Cartesian plane.

1. 2x – y = 4

What’s New

This module focuses on describing the graph of linear equations in two

variables in terms of its intercepts and slope as well as its uses in real life.

Activity 2: Let’s graph!

Direction: Plot the given ordered pairs on a Cartesian plane and connect it to
draw its graph.
1. (-3, 2) and (4, -5)
2. (2, 6) and (-1, -5)

3. (1, 4) and (-5, 4)

4. (-6, -2) and (-6, 5)

What is It
In this portion, I will show you how to graph linear equations in two variables
using its intercepts and slope. I will also show you here the different graphs of
linear equations in two variables using its intercepts and slope. So, it’s time to
gear up your mind with the new topic for today’s lesson.

Example 1: Graph 2x – y = 4.
Step 1: If your equation is in standard form, change it first in slope- intercept form.

Linear Equation

2𝑥 − 2𝑥 − 𝑦 = 4 − 2𝑥 Add -2x to both sides of the equation.

Arrange and Simplify

(-1) Multiply both side of the equation with -1.
Final answer

Step 2: Identify the y- intercept and slope of the equation. Since your equation is
now in slope- intercept form, it would be easy for you to identify the slope and
yintercept.

Remember:

and b ∈ℜ, and m ≠ 0.

Slope-Intercept form: y = mx + b, where m is the slope and b is the y-intercept, m
 So, in the linear equation =𝟐𝒙−𝟒 , our slope is 2 and our y – intercept is -4
(which has an ordered pair of (0, -4).

Step 3
: Locate the-y
intercept of
-4 or (0,-4) on the Cartesian plane.

� 𝑖� � 2
�= .
� 𝑢𝑛 1
Step 4
. Locate the next point by using the slope=
��

�
The next point is either (1,-2) or (-1, -6).

Step 5.

Plot either of these two points.

or

Step 6. Connect the two points using a straight line.

or
Example 2: Graph 3x + 2y = 6.
Step 1: If your equation is in standard form, change it first in slope- intercept form.
3𝑥 + 2𝑦 = 6 Linear Equation

3𝑥 − 3𝑥 + 2𝑦 = 6 − 3𝑥 Add -2x to both sides of the equation. 2𝑦 =

−3𝑥 + 6 Arrange and Simplify

( )(2𝑦) = (−3𝑥 + 6)( ) Multiply both side of the equation with -1.
−𝟑
𝒚= 𝒙+𝟑 Final answer

Step 2: Identify the y- intercept and slope of the equation.

Since your equation is now in slope- intercept form it would be easy for you to
identify the slope and y-intercept.

Remember:

yintercept, m and b ∈ℜ, and m ≠ 0.

Slope-Intercept form: y = mx + b, where m is the slope and b is the

−𝟑
So in the linear equation = 𝒙 + 𝟑, our slope is and our y – intercept is

3 (which has an ordered pair of (0, 3)).

Step : Locate the-intercept

y of 3 or (0, 3) on the Cartesian plane.
3

���� −3
�� = .
�� slope=
�� � 2
Step . Locate the next point by using the
��
4 �
The next point is either (1,-2) or (-1, -6).
Step 5. Plot either of these two points.

Step 6. Connect the two points using a straight

line.

or

Example 3: Graph x = 5.
Step 1: Construct table of values for the linear equation.
You may assign two values for y, say 4 and -2.

x
y 4 -2

Step 2: Solve for the values of x given the assigned values of y.

a. Let y=4, so

x + 0y = 5 Equation

x + 0(4) = 5 Substitute y = 4

x=5 Multiply and Simplify

b. Let x=-2, so

x + 0y = 5 Equation
x + 0(-2) = 5 Substitute y = -2
x=5 Multiply and Simplify

Step 3: Complete the table of values.

x 5 5
y 4 -2
Thus, the ordered pairs are (5,4) and (5, -2)

Step 4: Plot the points on the Cartesian plane.

Step 5: Draw a line through the points.

Thus, this is the graph of x = 5.

As you can observe, there are four different graphs of linear equations.

An increasing line from left to right.

The linear equation with this graph has a
positive slope.
A decreasing line from left to right.
The linear equation with this graph has a
negative slope.
 A horizontal line
which is the
graph of y = b. The
line that is
perpendicular with
the y- axis. It also
has a zero slope.

A vertical line which is the graph of x

= a. The line that is perpendicular
with the x- axis. It also has an
undefined slope.

What’s More

Let us try to answer this activity about describing linear equations using its
intercepts and slope.

Activity 3: Match it down

Direction: Match each linear equation to the description of its graph from choices
A to D. Write the linear equations in the appropriate column.

A. An increasing line from left to right.

B. A decreasing line from left to right.
C. A horizontal line.
D. A vertical line.
𝑦 = 30
𝑥=9
3𝑥 + 6𝑦 = 24 𝑦=7 𝑥 = 15

A B C D
What I Can Do
At this point, we are now going to apply the behaviour of the graph of linear
equations using its intercepts and slope in real-life
situation.

Activity 5: Let’s exercise

Direction: Read the situation below and answer the questions that follow.

Problem: Rhien burns 6 calories per minute when walking briskly and 12 calories per
minute when running.

a. Write an equation to represent the number of minutes Rhien must walk

and run to burn a total of 240 calories.
_______________________________________________________________
b. Identify the y- intercept and slope of your equation.
_______________________________________________________________

c. Graph the linear equation

d. Describe the behaviour of the graph.

____________________________________________________________________
____________________________________________________________________
Assessment

Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a
separate sheet of paper.

Great job! Let us see how far have you learned from the very start of our
lesson by answering the activity below.

Direction: Encircle the letter of the correct answer.

1. What is the y- intercept of 4x + y = -7?

a. −4

b. 4
c. −7
d. 7
Additional Activities
In this portion, another activity will be given to you as your assignment. This
will help you improve your retention of learned concepts. Now, use your knowledge
of slope and y- intercept to graph the given linear equations on the provided
coordinate plane.