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UNIT 1B LESSON 2 REVIEW OF LINEAR FUNCTIONS

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Equations of Lines The horizontal line through the point (2, 3) has equation The vertical line through the point (2, 3) has equation y = 3 x = 2 The vertical line through the point (a, b) has equation x = a since every x - coordinate on the line has the same value a. Similarly, the horizontal line through (a, b) has equation y = b

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Finding Equations of Vertical and Horizontal Lines Vertical Line is x = – 3 Horizontal Line is y = 8

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Y 1 = 2x + 7 xY = 2x + 7 y – intercept (, ) Slope y-intercept form y = mx + b slope y-intercept (0, b) EXAMPLE 2: Reviewing Slope-Intercept Form of Linear Functions

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Unit 1B Lesson 2 Page 1 EXAMPLES State the slopes and y -intercepts of the given linear functions. y = 4x slope = m = _______ y -intercept (, ) 3. y = 3x – 5 slope = m = _______ y -intercept (, ) 4. = slope = m = _______ y -intercept (, ) 6. slope = m = _______ y -intercept (, ) 6. 4 3 ⅓ 0, 0

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General Linear Equation Although the general linear form helps in the quick identification of lines, the slope-intercept form is the one to enter into a calculator for graphing. y = – ( A / B ) x + C / B By = – Ax + C Ax + By = C

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Analyzing and Graphing a General Linear Equation Example 7

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Unit 1B Lesson 2 Page 1 EXAMPLES State the slopes and y -intercepts of the given linear functions. x + 2y = 3 slope = m = _______ y -intercept (, ) 8. 0, 3 / 2 9. 0, 4 / 3

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Step 2: Find the equation b = 7

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Step 3: Find the equation

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EXAMPLE 12 Write the equation for the line through the point (– 1, 2) that is parallel to the line L: y = 3x – 4 Step 1: Slope of L is 3 so slope of any parallel line is also 3. Step 2: Find b. Step 4: Graph on your calculator to check your work. Use a square window. Y 1 = 3x – 4 Y 2 = 3x + 5 (0, 5) (0, – 4)

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Step 2: Solve for b using the point (10, – 1)

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EXAMPLE 14 Write the equation for the line through the point (– 1, 2) that is perpendicular to the line L: y = 3x – 4 Step 2: Find b.

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Step 1: Find the slope Step 2: Solve for b using either point Step 3: Find the equation (7, – 2) (– 5, 8)

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EXAMPLE 16 Write the slope-intercept equation for the line through (– 2, –1) and (5, 4). (5, 4) (– 2, – 1)

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Finish the 5 questions in Lesson #2

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