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2 – 4: Writing Expressions of Lines (Day 1 ) Objective: CA Standard 1: Students solve equations and inequalities involving absolute value.

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Writing Linear Equations Slope - Intercept Form: Given the slope m and the y-intercept b, use this equation Point – Slope Form: Given the slope m and a point (x 1, y 1 ), use this equation:

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Two Points: Given two point (x 1, y 1 ), and (x 2, y 2 ), use the formula to find the slope m.

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Example 1: Writing an Equation Given the slope and y-intercept.

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From the graph of the line determine the slope. m = 3/2 What is the y-intercept? (0, -1) What is an equation of this line? y = mx +b y = 3/2 x – 1

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Example 2 Write an equation of the line that passes through (2, 3) and has a slope of – ½. Use the point – slope form

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Example 3 Write an equation of a line that passes through (3, 2) and is parallel to the line y = -3x +2. If two lines are parallel they have the same slope. Let m = -3 and (x 1, y 1 ) = (3, -2)

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Use the point slope form.

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Write an equation of a line that passes through (3, 2) and is perpendicular to the line y = -3x +2. If two lines are perpendicular then the product of their slopes is –1. Example 4

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Use the point slope form find the equation of the line Let m 1 = -3 m 1 m 2 = -1 -3 m 2 = - 1 m 2 = -1/-3 m 2 = 1/3

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Example 5: Write an equation of a line that passes through (-2, -1) and (3, 4) Find the slope:

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Use the point slope form.

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Example 6: Writing and using a Linear Model. In 1984 Americans purchased an average of 113 meals or snacks per person at restaurants. By 1996 this number was 131. Write a linear model for the number of meals or snacks purchased per person annually. Then use the model to predict the number of meals that will be purchased per person in 2006.

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Average rate of change

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Verbal Model: Labels Number of Mealy Number in 1984113 Average Rate of change 1.5 Year since 1984t = 2006 –1984 t = 22

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y = 113 + 1.5 t y = 113 + 1.5 (22) y = 113 + 33 y = 146 Algebraic Model

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Home work page 95 14 – 42 even, and 61

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