This document provides an overview and examples of determining the equation of a line given different parameters in a graph of linear equations in two variables. It discusses finding the equation given two points, the intercepts, a point and slope, a slope and y-intercept, and includes examples of determining the equation from information provided and a short quiz to check understanding.

1. Graphs of Linear
Equations in Two
Variables
Powerpoint by: Cedric Lyoid J. Cabila
Lesson by: Archanjail A. Zaragosa

2. Graphs of Linear
Equations in Two
Variables
Lesson

3. Determine the Equation
of a Line Given Two
Points.

4. Determine the Equation of a Line Given Two
Points.
Solution : 𝒚 − 𝒚 𝟏 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(𝒙 − 𝒙 𝟏) Given: (-2,-2)(4,5)
𝑦 − (−2) =
5− −2
4− −2
(𝑥 − −2 )
𝒚 + 𝟐 =
𝟔
𝟕
𝒙 + 𝟐
𝒚 + 𝟐 =
𝟕
𝟔
𝐱 +
𝟏𝟒
𝟔
𝟔
𝟔𝒚 + 𝟏𝟐 = 𝟕𝒙 + 𝟏𝟒
𝟕𝒙 − 𝟔𝒚 = −𝟐

5. Determine the Equation
of a Line Given the
Intercepts.

6. Determine the Equation of a Line Given the
Intercepts.
Solution:
𝒙
𝒂
+
𝒚
𝒃
= 𝟏 Given: (6, 0) (0, -4)
𝒙
𝟔
+
𝒚
−𝟒
= 𝟏
𝒙
𝟔
+
𝒚
−𝟒
= 𝟏 𝟏𝟐
𝟐𝒙 − 𝟑𝒚 = 𝟏𝟐
𝒚 =
𝟐
𝟑
𝒙 − 𝟒

7. Determine the Equation
of a Line Given a Point
and a Slope of the Line.

8. Determine the Equation of a Line Given a Point
and a Slope of the Line.
Solution: 𝒚 − 𝒚 𝟏 = 𝒎(𝒙 − 𝒙 𝟏) Given :m =-7 and (-1,-3)
𝒚 − (−𝟑) = 𝒎(𝒙 − (−𝟏))
𝒚 + 𝟑 = (−𝟕)(𝒙 + 𝟏)
𝒚 + 𝟑 = −𝟕𝒙 − 𝟕
𝒚 = −𝟕𝒙 − 𝟕 − 𝟑
𝒚 = −𝟕𝒙 − 𝟏𝟎
𝟕𝒙 + 𝒚 = −𝟏𝟎

9. Determine the Equation
of a Line Given a Slope
and a y-intercept.

10. Determine the Equation of a Line Given a
Slope and a y-intercept.
Solution: 𝒚 = 𝒎𝒙 + 𝒃 Given: m =-7 y-intercept= 8
𝒚 = (−𝟕)𝒙 + (8)
𝒚 = −𝟕𝒙 + 𝟖
𝟕𝒙 + 𝒚 = 𝟖

11. Quiz

12. Determine the equation
of the line in standard
form given the following
and choose the correct
answer.

13. m=2; (3,5)
2x + y = 10
- 2x + y = -10
8x + y = 4
6y – y = 9

14. (3, 4) and (6, 8)
3x + 4y = 253x + 4y = -25
7x + 9y = 169x – y = 3

15. x-intercept: 2; y-intercept:10
5x + y = 10
7x + 1y = -5
5y + x = 10
5x – 9y = 2

16. slope: 5/3; y-intercept: -9
5x + y = -27
7x + 6y = 155y + x = 10
8x – 2y = 2

17. WRONG!

18. CORRECT!
Q.2

19. CORRECT!

20. CORRECT!
Q.4

21. CORRECT! Next

22. Finish