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1. Linear equations
in two variables

2. What is a linear equation in two variables?
is an equation that can be described or can be
written in two form: Ax + By = C where A, B and
C are real numbers, A and B not both 0 or slope
intercept form y = mx + b where m and b are
also real numbers (where m is the slope and b is
the y- intercept.

4. A linear equation in two variables in standard for
can be transformed or rewritten into a slope
intercept form y = mx + b and vice versa.
To transform Ax + By = C into y or f(x) = mx + b
and vice versa it is important to recall the
properties of equality.

5. Properties of equality

6. addition property of equality (ape)
if the same number or terms is added to the left
and right members of an equation, the sums are
equal.
Example:
If a = b, then a + c = b + c

7. Remember: We must divide BOTH
sides of the equation by two to keep
the equation balanced!
2b = 18
The multiply by 2 and divide by 2
cancel each other out.
2b ÷ 2 = 18 ÷ 2
b = 9
2b ÷ 2 = 18 ÷ 2
Second step: Think about what the opposite operation to
multiplying is.
multiplication property of equality
(mpe)
Solve the linear equation: 2b = 18
First step: Think about what 2b means.
DIVIDING!
2b means 2 x b (2 groups of b)
The opposite of multiplying is ...
If the same number or terms is multiplied to the left
ad members of an equation, the products are equal.
Example:
If a = b, then ac = bc

8. diviision property of equality (dpe)
If the same number is divided to the left and right
members of an equation, the quotients are equal.
Example:
If a = b, then a = b
c c

11. To transform y = mx + b into Ax + By = C transfer
the terms from one side to another to combine
similar terms. it is clearly emphasized that the x
and y terms are written at the left side of an
equation while the constant term are written at the
right side of an equation.

13. Practice
Rewrite the equation y = 12x + 3 in
the form Ax + By = C.

14. QUIZ
1.Rewrite the equation in the form
y = mx + b and identify the values
of m and b.
5x + 2y = 7