2. • Identify if the given equation is a linear
equation in two variables;
• Determine if an ordered pair is a
solution of a given linear equation;
• Plot a graph of a linear equation; and
• Solve problems involving linear
equations in two variables.
Objectives
3. Rene
Descartes
Rene Descartes introduced the
Cartesian Coordinates plane that
involves the construction of two
perpendicular number lines, one
horizontal and vertical, whose point of
intersection called origin.
4. a.) A vertical line is named y-axis
and the horizontal line is x-axis
b.) The two axis divide the plane
into four quadrants that are
numbered counter clockwise
direction. (I, II, III, IV)
c.) Every point in the plane can be
described in terms of an ordered
pair (x, y) or (abscissa, ordinate).
• Under the first quadrant the
value of X is positive as well as
the value of Y.
• Under the second quadrant the
value of X is negative while the
value of Y is positive.
• Under the third quadrant both
values of X and Y is negative
• Under the fourth quadrant the
value of X is positive while the
value of Y is negative.
5. Linear Equation in
Two Variables
A linear equation in two variables is an equation
that can be written in the standard form
Ax + By = C, where a, b and c are real numbers
and a and b are not both zero; and the exponent
of the variables must be 1.
Example: 4x = 9 + 2y
4x – 2y = 9
a = 4, b = -2 and c = 9
6. y = 5x + 3
x -3 0 𝟏
𝟓
3
y
Find y if x is -3, 0,
𝟏
𝟓
, 3
7. 3x – y + 1 = 0
To graph the linear equation:
a. Find at least two solutions in the equation.
b. Plot the solution of the equation.
c. Connect the points to straight line.
x -1 0 1 2
y
8. 2x + y = 12
x -3 0 3 6
y
Try it!
Find the solution of the equation and graph.
9. Cristy had already walked 5 kms. And
continue walking 3 kms per hour. Write the
equation that shows the relation between the
distance and the time after 10 hours, how far
does Cristy walked?
Solution:
Let x be the time (hours)
Let y be the distance (km)
y = 3x + 5
y = 3(10) + 5
y = 30 + 5
y = 35 km
10. Solution:
Let x = the number of permanent markers Tina can buy.
Let y = the number of cartolinas she can buy.
Equation 45x + 9y = 180
45x + 9y = 180
9y = 180 – 45x
y = 20 – 5x
x 1 2 3 4
y = 20 – 5x
Tina went to the bookstore to buy some school supplies. She
needs to buy some permanent markers that cost Php45.00
each and some cartolinas for Php9.00 each. How many each
kind can she buy for Php180.00?
11. ASSIGNMENT:
In a ½ sheet of paper, answer the following:
1. What is SLOPE?
2. Give the four kinds of Slope.
