1. Objective: To write linear equations given two points
Ch 5.3
Objective:
To write linear equations given two points

2. Steps for Solving
1) Use the two points to find the slope (use the formula or use rise/run). 2) Input the slope and ONE of the points: a) into the point-slope form: y – y1 = m(x – x1) and then solve for “y” or b) Into the slope-intercept form: y = mx + b to solve for “b” then input the slope and “b” into y = mx + b

3. Example 1: using slope-intercept (y = mx + b)
Write the equation of the line which contains:
(3, 5) and (-3, 3)
(x, y)
y = mx + b
y2- y1 - 2 5 3 1 1
Slope (m) = = = =
x2- x1
y = x + b - 6 3 3
(-3) 3 1
5 = (3) + b 3 3
5 = b
b = 5 -
b = 4 3 3 3 1
y = x + 4 3

4. Example 1: using point-slope [y –y1= m(x – x1)]
Write the equation of the line which contains:
(3, 5) and (-3, 3)
(x, y)
y – y1 = m (x – x1)
y2- y1 - 2 5 3 1
Slope (m) = = = =
x2- x1 - 6 3 3
(-3) 1 3
y = (x ) 5 3
1 x 3
- 1
y – 5 = 1
y = x + 4
+ 5
+ 5 3

5. -3 = b Example 2: using slope-intercept (y = mx + b)
Write the equation of the line which contains:
(0, -3) (4, 8)
y = mx + b
(x, y) 11
y = x + b
y2- y1 4
Slope (m) =
x2- x1 11
8 = (4) + b 4
8 - -3 11
Slope (m) = =
4 - 0
8 = b 4 11
m =
-3 = b 4
b = -3 11
y = x - 3 4

6. Example 2: using point-slope [y – y1 = m (x – x1)]
Write the equation of the line which contains:
(0, -3) (4, 8)
(x, y)
y2- y1
8 - -3 11
Slope (m) = = =
x2- x1
4 - 0 4 11 4
y = (x ) 4 8
y – 8 =
11 x - 11 4
+ 8
+ 8
y = x - 3 11 4

7. -12 -12 Use the x-y chart below to write a linear
equation that satisfies all the points. x y
y = mx + b +2 +6
y = 3x + b +3 +9
10 = 3(4) + b +2 +6 +5
+15
10 = 12 + b
y2- y1
10 - 4
-2 = b
m = =
x2- x1
4 - 2 6
m = = 3
y = 3x - 2 2