1. Writing Linear Equations from Graphs

2. Learning Targets
From a graph, write an equation in slope-intercept form.
From a graph, write an equation in point-slope form.

3. Writing Equations: Procedure Point Slope form
1. Identify any ordered pair on the line
2. Identify the slope
Option 1: slope formula
Option 2: “rise over run” – triangle method
3. Plug into the point slope equation

4. Writing Equations: Example 1 Point Slope
Write the equation of the line
Example point: (−4, 2)
Slope: 2 points (−4, 2) & (0, 3)
3−2 0−−4 = 1 4
𝑦−2= 1 4 (𝑥+4)

5. Writing Equations: Example 2 Point Slope
Write the equation of the line
Example Point: (−2, 2)
Slope: −1, 1 & (0, 0)
0−−1 0−1 =− 1 1 =−1
𝑦−2=−1(𝑥+2)

6. Writing Equations: Example 3 Point Slope
Write the equation of the line
Example Point: (3, 1)
Slope: 0, 2 & (3, 1)
1−2 3−0 =− 1 3
𝑦−1=− 1 3 (𝑥−3)

7. Writing Equations: Procedure Slope Intercept form
1. Write in point-slope form first
2. Manipulate into slope-intercept form

8. Writing Equations: Example 1 slope intercept
Write the equation of the line
Point (0,3)
Slope: 2 points (−4, 2) & (0, 3)
3−2 0−−4 = 1 4
𝑦−3= 1 4 𝑥−0
𝑦= 1 4 𝑥+3

9. Writing Equations: Example 2 Slope Intercept
Write the equation of the line
Point (0,0)
Slope: −1, 1 & (0, 0)
0−−1 0−1 =− 1 1 =−1
𝑦−0=−(𝑥−0)
𝑦=−𝑥

10. Writing Equations: Example 3 Slope Intercept
Write the equation of the line
Point (0,2)
Slope: 0, 2 & (3, 1)
1−2 3−0 =− 1 3
𝑦−2=− 1 3 𝑥−0
𝑦=− 1 3 𝑥+2

11. Writing Equations: Example 4 Slope Intercept
Write the equation of the line
Point (5,0)
Slope: 0, 7 & (5,0)
0−7 5−0 =− 7 5
𝑦−0=− 7 5 (𝑥−5)
𝑦=− 7 5 𝑥+7

12. Writing Equations: Example 5 Slope Intercept
Write the equation of the line
Point: (-2, 1)
Slope: 0, −3 & (−2, 1)
1−−3 −2−0 = 4 −2 =−2
𝑦−1=−2 𝑥+2
𝑦−1=−2𝑥−4
𝑦=−2𝑥−3