Download 2.2 Linear Equations

Linear Equations
Objectives:
-Find slope of a line
- write 3 different forms of linear
equations
Ms. Olifer
SLOPE
RISE
RUN
Slope Formula
Given points (X1,Y1) and (X2,Y2)
rise
m
run
y 2  y1
x 2  x1
Is y 2  y1 the same as
x 2  x1
y1  y 2
x1  x 2
?
Example
( 4 , 0 ) and ( 7 , 6 )
(X1,Y1)
(X2,Y2)
y 2  y1
60

m
2
74
x 2  x1
Example
( -6 , 5 ) and ( 2 , 4 )
(X1,Y1)
(X2,Y2)
1
y 2  y1
45


m
8
x 2  x1 2  6
Example
( 5 , 2 ) and ( -3 , 2 )
(X1,Y1)
(X2,Y2)
0
y 2  y1
22


m
x 2  x1  3  5  8
0
Example
( 2 , 7 ) and ( 2 , -3 )
(X1,Y1)
(X2,Y2)
 10
y 2  y1  3  7
 undefined


m
0
22
x 2  x1
Recap of slope
Linear Forms of Linear Equations
Standard Form (AX + BY = C)
1) A and B cannot be fractions.
2) A cannot be negative
y = 3x – 5
y – 3x = – 5
– 3x + y = – 5
3x – y = 5
FINDING INTERCEPTS
To find y-intercept, set x = 0
Y-intercept (0,-5)
To find x-intercept, set y = 0
X-intercept (5/3,0)
Linear Forms of Linear Equations
Slope Intercept Form (y = mx + b)
1) Y is isolated on one side.
2) Y is positive
x – 2y = 6
–2y = – x + 6
y = ½ x + 6/-2
y= ½x–3
FINDING INTERCEPTS
To find y-intercept, set x = 0
Y-intercept (0,-3)
To find x-intercept, set y = 0
X-intercept (6,0)
Find a line
|| to 2x + 4y = -8
and passes thru (8,3)
• First find
slope
• 2x + 4y = -8
• 4y = -2x – 8
• y=-½x–2
• Slope
•
•
•
•
•
•
Use y = mx + b
y = - 1/2x + b
Plug in point
3 = - ½ (8) + b
FINAL
3 = -4 + b
EQUATION
7=b
y = mx + b
y=-½x+7
Find a line
Perpendicular to 3x – 2y = 10
and passes thru (-6,2)
•
•
•
•
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
FINAL EQUATION
-2 = b
y = mx + b
y = -2/3x - 2
Find a line
That has slope = 2
and passes thru (-4,7)
•
•
•
•
•
•
Use y = mx + b
y = 2x + b
Plug in point
7 = 2 (-4) + b
7 = -8 + b
FINAL EQUATION
15 = b
y = mx + b
y = 2 x + 15
Find a line
That has x-intercept = (5,0)
and y-intercept (0,-3)
• First find
slope
• m
30

05
• 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
First Let’s Review . . .
Graphing Linear Equations
Graph x = 3
Graph y = -3
Graph
Y = -3/4 x + 2
Y = mx + b
m = slope
b = y-intercept
m = -3 / 4
b=2
1)
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.