This document provides examples for rewriting linear equations between the slope-intercept form (y=mx+b) and standard form (Ax + By = C). It begins with examples of rewriting equations from standard form to slope-intercept form and identifying the slope (m) and y-intercept (b). Then it provides examples of rewriting from slope-intercept form to standard form. Finally, it provides a series of practice problems for rewriting linear equations between the two forms.

1. Linear equation
Writing linear equation
ax + by = c in the form y = mx + b
and vice versa

2. Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile

3. Objectives:
1. Identify standard form and
slope-intercept form.
2. Rewrite linear equation in
slope- intercept form to
standard form
and vice versa
2. Answer with accuracy.

4. Drill/ Fixing Skills
Direction:
Identify following linear equations whether in standard form or
slope- intercept form.
1. 5𝑥 + 4𝑦 = 7
2. 2x – 6 = y
3. 𝑥 − 7𝑦 = 0
4. 𝑦 =
3
4
𝑥 + 3

5. A linear equation is an equation in two variables
which can be written in two forms:
Standard Form or
General Form:
where A, B and C∈ℜ, A
≠ 0 and B ≠ 0; and
Slope-Intercept Form:
where m is the slope and
b is the y-intercept, m
and b∈ℜ, and m ≠ 0.
Ax + By = C
y = mx + b

6. Illustrative Examples:
Rewriting linear equation in slope- intercept form
to standard form and vice versa

7. DAY 1
Direction: Write the following linear equations in the form y = mx
+ b. Identify m and b.
1. 5x + 3y = 1
Solution:
3y = -5x + 1 Add -5x to both sides
y =
5𝑥
3
+
1
3
Divide both sides by 3
m =-
5
3
, b =
1
3

8. 2. 3x – 4y – 12 = 0
Solution:
-4y = -3x + 12 Add -3x + 12 to both sides
y =
−3𝑥
−4
+
12
−4
Divide both sides by -4
y =
3𝑥
4
- 3
m =
3
4
,b = -3
DAY 1
Direction: Write the following linear equations in the form y =
mx + b. Identify m and b.

9. DAY 1
3.Rewrite the equation 3x – 5y = 10 in the form y = mx + b.
Determine its slope and y-intercept.
Solution:
3x – 5y = 10 Given
-5y = -3x + 10 Addition Property of Equality
−5𝑦
−5
=
−3𝑥
−5
+
10
−5
Division Property of Equality
y =
3𝑥
5
- 2
The slope is
3
5
and the y-intercept is -2.

10. DAY 2
4. Rewrite the equation y = 12 x + 3 in the form
Ax + By = C?
Solution:
y = 12x + 3 Given
-12x + y = 3 A PE
12x - y = - 3 MPE

11. Day 2
Write the following equations in the form Ax + By = C
5. y =
1
2
x -
2
3
Solution:
y =
1
2
x -
2
3
Multiply all the terms by 6 (LCD)
6y = 3x - 4
-3x + 6y = -4 Add -3x to both sides
or 3x – 6y = 4

12. Day 2
Write the following equations in the form Ax + By = C
6. x +
3
4
= 2y
Solution:
x +
3
4
= 2y Multiply all the terms by 4
4x + 3 = 8y Add -8 to both sides
4x – 8y + 3 = 0
4x – 8y = -3 Add -3 to both sides

13. To Do…
1. 2x + y = 9
2. x + 2y = 4
3. 3x – y = 2
4. 5x + 2y = 7
5. -3x + 3y – 1 = 0
6. y = -x + 4
7. y = -2x + 6
8. y = 5x + 7
9. y = 3x – 8
10. y = 12x
DAY 1:
Rewrite the following equations in
the form y = mx + b and identify the
values of m and b.
DAY 2:
Rewrite the following equations in
the form Ax + By = C.

15. Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module