Writing Linear Equations from Graphs

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

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

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)

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)

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)

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

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

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

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

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

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