Warm up 11-6
Find the slope between the points.
1. (9 , 0) ( 10, -3)
2. (-5 , 2) (-8, 2)
3. (11, 7) (4 , 0)
4. ( -4 , -2) ( 1, 2)
Unit 4 Day 5: Writing an
Equation Given Two
Points
Essential Questions: How do we write the
equation of a line given two points on the line?
Steps for Writing an Equation Given
Two Points
1. Find the slope of the line using the slope
y2 - y 1
formula:
x2 - x 1
2. Plug in the slope and one of your points
into the slope-intercept equation of a line
(y = mx + b) and solve for b.
3. Rewrite your complete equation using m
and b.
Example 1: Write the equation of the line passing through
x1 y1
y2 - y1
x2 - x1
y = mx + b
x2 y2
4 - (-1)
-2 - (-3)
4+1
-2 + 3
-1 = 5(-3) + b
5
1
-1 = -15 + b
Final equation: y = 5x + 14
m=5
b = 14
Example 2: Write the equation of the line passing through
x1 y1
y2 - y1
x2 - x1
y = mx + b
x2 y2
6-8
4-2
-2
2
8 = -1(2) + b
m = -1
8 = -2 + b
Final equation: y = -1x + 10
b = 10
Example 3: Write the equation of the line passing through
x1 y1
y2 - y1
x2 - x1
x2 y2
6 - (-9)
3 - (-6)
6+9
3+6
15
9
5
m=
3
-30
5
y = mx + b -9 = (-6) + b -9 =
+ b -9 = -10 + b
3
3
b=1
5
Final equation: y =
x+1
3
Example 4: Write the equation of the line passing through
x1 y1
y2 - y1
x2 - x1
y = mx + b
x2 y2
4-4
3-5
0
-2
4 = 0(5) + b
m=0
4=0+b
y = 0x + 4
Final equation: y = 4
b=4
Example 5: Write the equation of the line passing through
x1 y1
y2 - y1
x2 - x1
x2 y2
1-5
2-2
-4
m = undefined
0
Look at the x values: what does x equal both times?
Final equation: x = 2
Summary
Essential Questions: How do we write the
equation of a line given two points on the line?
Take 1 minute to write 2 sentences answering the essent