1. Linear Equations in Two Variables
Section 1.2
Linear Equations in Two Variables

2. What you should learn
How to use slope to graph linear equations in two variables
How to write linear equations in two variables
How to use slope to identify parallel and perpendicular lines
How to use linear equations in two variables to model and solve real-life problems

3. Slope describes the direction of a line.

4. Guard against 0 in the denominator
Why is this needed?
Slope
If x1  x2, the slope of the line through the distinct points (x1, y1) and (x2, y2) is
Guard against 0 in the denominator

5. Find the slope between (-3, 6) and (5, 2)
x-axis
y-axis
Rise -4 -1 = =
Run 8 2

6. Find the slope between (-3, 6) and (5, 2)

7. Find the Slope
Green
(3, 9)
Blue
(11, 2)
Red
(5, -2)

8. Find the slope between (5, 4) and (5, 2).
STOP
This slope is undefined.

9. Find the slope between (5, 4) and (5, 2).
x-axis
y-axis
Rise -2
Undefined = =
Run

10. Find the slope between (5, 4) and (-3, 4).
STOP
This slope is zero.

11. Find the slope between (5, 4) and (-3, 4).
x-axis
y-axis
Rise
Zero = =
Run -8

12. From these results we can see...
The slope of a vertical line is undefined.
The slope of a horizontal line is 0.

13. Graph the line that goes through (1, -3) with
x-axis
y-axis
(1,-3)

14. Using Slope to Graph
Graph the line that contains (4, 5) and has a slope of 3/2.
(8, 11)
(6, 8)
(4, 5)

15. Using Slope to Graph
Graph
(0, 8)
(4, 5)
(8, 2)

16. Slope

17. Point-Slope
Slope
Point

18. Slope Intercept
Slope
Y-intercept

19. Standard Form of a Line

20. Parallel Lines
Two distinct nonvertical lines are parallel if and only if their slopes are equal.
That is,

21. Parallel
Find the slope-intercept form of the line that passes through (2,1) parallel to
2x – 3y = 5.

22. Perpendicular
Find the slope-intercept form of the line that passes through (2,1) perpendicular to
2x – 3y = 5.

23. Homework Page 21 1, 9-27 odd 39- 45 odd, 51-79 odd