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AFDA – Unit 2: Linear Functions Pt 2 Day 1 Notes: Graphing Linear Equations Name: _________________ Block: _____ Date:_______ Today you will review… domain and range of a linear function how to graph linear equations in: o slope-intercept form o standard form o special cases Key Terms X-Intercept: The point where a graph crosses the ____________________. Y-Intercept: The point where a graph crosses the ____________________. Domain All the ____________________. Read from ___________________________. Range All the ____________________. Read from ___________________________. The domain and range of a LINEAR FUNCTION will always be _________________. 𝑦=𝑥 Domain: (−∞, ∞) Range: (−∞, ∞) Three Ways to Graph Lines Method 1: Using a table of values Method 2: Using slope and y-intercept Method 3: Using x- and y- intercepts Method 1: Table of Values When it looks like: 𝑦 = 𝑚𝑥 + 𝑏 Easiest when 𝑚 is an ____________________ Examples. 1. 𝑦 = 2𝑥 − 3 𝑥 2. 𝑦 = −3𝑥 + 4 𝑦 Domain: 𝑥 Range: 3. 𝑦 = 4𝑥 + 2 𝑥 Domain: How to Use: 1. Pick at least _____ numbers for x and plug into the function. 2. Get _____ values. 3. __________. 4. Connect the points using a straight edge. 𝑦 Domain: Range: 4. 𝑦 = −𝑥 − 2 𝑦 𝑥 Range: Domain: 𝑦 Range: Method 2: Using Slope and Y-Intercept When it looks like: 𝑦 = 𝑚𝑥 + 𝑏 Especially when 𝑚 is a ____________________ Examples. 3 1. 𝑦 = − 𝑥 + 2 How to Use: 1. Identify the __________ (m) and the __________ (b). 2. Plot “b” (think BEGIN) 3. Using __________ (m), MOVE from b and plot next point. 4. Connect the points using a straight edge. 2 2. 𝑦 = 𝑥 4 5 𝑚= 𝑚= 𝑏= 𝑏= Domain: Range: Domain: 3. 2𝑦 = −𝑥 + 6 4. 3𝑦 = 5𝑥 − 9 𝑚= 𝑚= 𝑏= 𝑏= Domain: Range: Domain: Range: Range: Method 3: Using X- and Y-Intercepts When it looks like: 𝐴𝑥 + 𝐵𝑦 = 𝐶 How to Use: 1. Solve for the ____________________ by plugging in 0 for 𝑦. 2. Plot the x-intercept. 3. Solve for the y-intercept by plugging in 0 for _______. 4. Plot the y-intercept. 5. Connect the points using a straight edge. aka Examples. 1. 3𝑥 − 2𝑦 = −6 2. 3𝑥 + 2𝑦 = −12 𝑥 − 𝑖𝑛𝑡: 𝑥 − 𝑖𝑛𝑡: 𝑦 − 𝑖𝑛𝑡.: 𝑦 − 𝑖𝑛𝑡.: Domain: Range: Domain: 3. 8𝑥 = 24 + 6𝑦 4. 𝑥 = 4 − 𝑦 𝑥 − 𝑖𝑛𝑡: 𝑥 − 𝑖𝑛𝑡.: 𝑦 − 𝑖𝑛𝑡.: 𝑦 − 𝑖𝑛𝑡.: Domain: Range: Domain: Range: Range: Special Cases: HOY and VUX H0Y VUX Domain: (−∞, ∞) Domain: equation of line, 𝑥 = # Range: equation of line, 𝑦 = # Range:(−∞, ∞) Examples. 1. 𝑦 = −2 2. 𝑥 = −2 Domain: Domain: Range: Range: 3. 𝑦 = 4 4. 𝑥 = 4 Domain: Domain: Range: Range: 5. 𝑦 = 3 6. 𝑥 = 3 Domain: Domain: Range: Range: