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Lesson 5-5 Standard Form Sept. 24, 2014 Daily Learning Target • I will write and graph equations in standard form. Intercepts • Think about what the word “intercept” means. • What does the y-intercept look like? • What does the x-intercept look like? Standard Form • Any linear equation can be expressed in the form Ax + By = C where A, B, and C are integers and A and B are not both zero. This is called standard form. An equation that is written in point-slope form can be written in standard form. • Rules for Standard Form: • Standard form is Ax + By = C, with the following conditions: 1) No fractions 2) A is not negative (it can be zero, but it can't be negative). By the way, "integer" means no fractions, no decimals. Just clean whole numbers (or their negatives). Example 1 • Find the x- and y-intercepts of the graph of 3x + 4y = 24 We will substitute 0 for the x and y (at different times) to identify the intercepts. x-int. = 8 x=8 and y-int. = 6 y=6 You Try • What are the x- and y-intercepts of the graph of each equation. 1) 5x – 6y = 60 x = 12; y = -10 2) 3x + 8y = 12 x = 4; y = 3 2 Example 2 • What is the graph of x – 2y = -2 • Find the x- and yintercepts. x = -2; y = 1 • Graph each intercept and connect the points You Try • What is the graph of 2x + 5y = 10? Graphing Horizontal and Vertical Lines • What is the graph of each equation? 1) x = 3 2) y = 3 You Try • What is the graph of each equation? 1) x = 2 2) y = -5 Transforming to Standard Form • What is y = - 3 x 7 + 5 written in standard form? • Step 1: Get rid of the fraction (distributive property) • Step 2: Get the x and y on the same side of the equal sign. Transforming to Standard Form • Write y – 2 = - 1 (x 3 + 6) • Step 1: Simplify to get rid of the parenthesis • Step 2: Get rid of the fraction • Step 3: Rearrange the equation to put x and y on the same side. Model • The iTunes store sells songs for $1 each and movies for $12 each. You have $60 to spend. Write and graph an equation that describes the items you can purchase. What are three combinations of numbers of songs and movies you can purchase? You Try • In the last example, suppose the store changed the price of movies to $15 each. What equation describes the number of songs and movies you can purchase for $60. • What domain and range are reasonable for the above equation? Explain. Homework • Workbook • Page 155 problems 3, 5, 6, 8, 9, 10-12, 17, 20 • Page 157 problems 1-5