1. 2.2 Linear Equations

2. SLOPE
SLOPE
RISE
RUN

3. Slope Formula
Given points (X1,Y1) and (X2,Y2)
Is the same as ?

4. Example ( 4 , 0 ) and ( 7 , 6 )
(X1,Y1) (X2,Y2)

5. Example ( -6 , 5 ) and ( 2 , 4 )
(X1,Y1) (X2,Y2)

6. Example ( 5 , 2 ) and ( -3 , 2 )
(X1,Y1) (X2,Y2)

7. Example ( 2 , 7 ) and ( 2 , -3 )
(X1,Y1) (X2,Y2)

8. Recap of slope

9. Linear Forms of Linear Equations Standard Form (AX + BY = C)
FINDING INTERCEPTS
A and B cannot be fractions.
A cannot be negative
To find y-intercept, set x = 0
Y-intercept (0,-5)
To find x-intercept, set y = 0
X-intercept (5/3,0)
y = 3x – 5
y – 3x = – 5
– 3x + y = – 5
3x – y = 5

10. Linear Forms of Linear Equations Slope Intercept Form (y = mx + b)
FINDING INTERCEPTS
Y is isolated on one side.
Y is positive
To find y-intercept, set x = 0
Y-intercept (0,-3)
To find x-intercept, set y = 0
X-intercept (6,0)
x – 2y = 6
–2y = – x + 6
y = ½ x + 6/-2
y = ½ x – 3

11. Find a line || to 2x + 4y = -8 and passes thru (8,3)
Slope intercept
First find slope
2x + 4y = -8
4y = -2x – 8
y = - ½ x – 2
Slope
Use y = mx + b
y = - 1/2x + b
Plug in point
3 = - ½ (8) + b
3 = b
7 = b
FINAL EQUATION
y = mx + b
y = - ½ x + 7

12. Find a line Perpendicular to 3x – 2y = 10 and passes thru (-6,2)
Slope intercept
First find slope
3x – 2y = 10
- 2y = -3x + 10
y = 3/2 x – 5
Slope
Use y = mx + b
y = -2/3 x + b
Plug in point
2 = -2/3 (-6) + b
2 = 4+ b
-2 = b c
FINAL EQUATION
y = mx + b
y = -2/3x - 2

13. Find a line That has slope = 2 and passes thru (-4,7)
Slope intercept
Use y = mx + b
y = 2x + b
Plug in point
7 = 2 (-4) + b
7 = b
15 = b
FINAL EQUATION
y = mx + b
y = 2 x + 15

14. Find a line That has x-intercept = (5,0) and y-intercept (0,-3)
Slope intercept
First find slope m
m = 3/5
Use y = mx + b
y = 3/5 x + b
Plug in point either one !
0 = 3/5 (5) + b
0 = 3 + b
-3 = b
FINAL EQUATION
y = mx + b
y = 3/5 x - 3

15. First Let’s Review . . .
Graphing Linear Equations

16. Graph x = 3

17. Graph y = -3

18. Graph Y = -3/4 x + 2 Y = mx + b m = slope b = y-intercept
m = -3 / 4 b = 2
Plot the y-intercept first
Starting from the y-intercept,
go up if + or down if –
Then go right.
3) Plot point and draw your line.

19. Graph 5x + 6y < 30
5x + 6y < 30
6y< -5x + 30
Y < -5/6 x +5

20. Graph 2x + 4y ≥ 16 2x + 4y ≥ 16 4y ≥ -2x + 16 Y ≥ -2/4 x + 4

21. Graph 5x - y < 8
5x – y < 8
– y < -5x + 8
y > 5x – 8