5-2B Two-Point Equation of a Line

Warm-up (IN)

Learning Objective: to determine the equation of a line through 2 given points.

Rewrite the equations in slope-intercept form and identify m and b.

545 1. xy m = -4/5

123 2. yx

2

144 3. xy

xy

24

4.

b = 1

m = -1/3 b = 4

m = -1 b = -1/8

m = 8 b = 0

15

4

xy

43

1

xy

8

1 xy

xy 8

NotesLearning Objective: to determine the equation of a line through 2 given points.

Ex 1 – Write the equation of the line through the points a. (-2,-1) and (2,3)

1st – find the slope

y=mx+b Need m and b!

3-(-1)

2-(-2)=

4= 1

4

2nd – substitute slope into y=mx+b y= 1x +b

3rd – pick a point to substitute for x and y

3= 1(2) +b

3= 2 +b

4th – solve for b

-2-2

1 =b

5th – plug m and b back into y=mx+b

y= x +1

Learning Objective: to determine the equation of a line through 2 given points.

b. (1,6) and (3,-4)

-4-6

3-1=-10

2= -5

y= -5x +b

6= -5(1) +b

6= -5 +b

+5+5

11=b

y= -5x +11

Learning Objective: to determine the equation of a line through 2 given points.

c. (64,-32) and (52,-28)

-28-(-32)

52-64=

4

-12=

-1

y= x +b

-28= (52) +b

-84= -52 +3b+52+52

-32=3b

y=

3-13

-13

-32

3=b

-13

x32

3-

HW – pg. 341 #21-28

Out – write the equation through

Summary – I think I understand…POW!!

(-5,2) and (-6,0)