1. Linear Equations

2. What makes a linear equation LINEAR?
An equation in one or more variables, each with an exponent of ONLY 1, where these variables are only added or subtracted.

3. So with that definition Which of these equations are linear?
x+y = 5
2x+ 3y = 4
7x-3y = 14
y = 2x-2
y=4
x2 + y = 5
x = 5
xy = 5
x2 +y2 = 9
y = x2 y 3

4. So with that definition Which of these equations are linear?
Not Linear
x+y = 5
2x+ 3y = 4
7x-3y = 14
y = 2x-2
y=4
x2 + y = 5
x = 5
xy = 5
x2 +y2 = 9
y = x2 y 3

5. If you had to describe a line what characteristics would you detail?x y x
Line A
Line B

6. Slope, Intercepts y x y x
Line A
Line B

7. Slopes
Positive
Negative
Horizontal
Vertical

8. Intercepts – where the line crosses the axes.y x y x
y-intercept=4
x-intercept=-3
x-intercept=-5
y-intercept=-5
Line A
Line B

9. Intercepts are actually points in the coordinate system.x y x
y-intercept=(0,4)
x-intercept=(-3,0)
x-intercept=(-5,0)
y-intercept=(0,-5)
Line A
Line B

10. Quadrants Review y II I x
III VI

11. Ordered Pairs Review : (x,y)II I
(-x,y)
(x,y)
III VI
(-x,-y)
(x,-y)

12. Linear Equations – What you should be able to identify for all lines.
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope

13. Slope Intercept Standard Horizontal Vertical y = mx + b Ax + By = C
Equation Forms
Slope Intercept
Standard
Horizontal
Vertical
y = mx + b
Ax + By = C
y = b
x = a

14. Slope-Intercept y = mx + b
y = ½ x + 5
y = -3x - 7
Slope
y-intercept

15. 3x – 2y = 9 4x + 2y = 16 Standard Form Ax + By = C
A, B, C are all integers with A > 0
3x – 2y = 9
4x + 2y = 16

16. Given our 4 example equations identify all of the following…
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope
y = ½ x + 5
y = -3x – 7
3x – 2y = 9
4x + 2y = 16

17. y = ½ x + 5 Slope intercept The Equation Form Rising Direction ½ Slope
-5/(½) = -10 -2
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope

18. y = -3x – 7 Slope intercept The Equation Form Falling Direction -3-7
- -7/(-3) = -7/3
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope

19. 3x – 2y = 9 Standard The Equation Form Rising Direction 3/2 Slope
-2/3
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope

20. 4x + 2y = 16 Standard The Equation Form Falling Direction -2 Slope 8
1/2
The Equation Form
Direction
Slope
y-intercept
x-intercept
Parallel Slope
Perpendicular Slope

21. What if you are just given two points on a line?
The slope formula
m =
Similar to Point-Slope Form
y – y1 = m(x – x1) or y2 – y1 = m(x2 – x1)
y2 – y1
x2 – x1

22. 1st – Find the Slope: y x
A(6,6)
B(-3,9)

23. 15 9 5 3
slope = ( ) ( ) = = y x
A(6,6)
B(-3,9)

24. 15 9 5 3
slope = ( ) ( ) = = y x
A(6,6)
B(-3,9)

25. Now substitute the slope and one point into the slope intercept form y = mx + b
m = 5/3 point (6,6)
6 = (5/3)(6 + b)
6 = 10 + (5/3)b
-4 = (5/3)b
-12/5 = b
Linear equation is y = (5/3)x – 12/3

26. 31 Linear Equations
On – Line Assignment