Standard Form of a Linear Equation

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Edith Conley
6 years ago
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1 Name: Date: Page 1 of 6 Standard Form of a Linear Equation The slope-intercept form of a line is. The standard form of a line is A + B = C. The parameters A, B and C are ma be an real numbers. Often the are integers. You have used the standard form of an equation with ou investigated ipods and points scored at basketball games. You can transform an equation in standard form into slope-intercept form b solving for. You can transform an equation in slope-intercept form into standard form b getting the constant term alone on the right side of the equal sign. Multipl the equation b a common denominator if necessar to clear fractions. If ou multipl or divide both sides of an equation in standard form b the same number, ou ll get an equivalent equation that is also in standard form. Here is an eample of a linear function that lends itself well to slope-intercept form: It costs $2 to open the St Vincent DePaul Soup for the evening meal regardless of the number of people served. The average meal cost per person is $4. What is the total cost of feeding people? Let be the number of people who eat, and let be the total cost. An equation to model this situation is. Here is an eample of linear function that lends itself well to standard form: Each ear, Norwich students make hundreds of cla soup bowls for a soup kitchen fundraiser known as the Empt Bowls Project. Then the public is invited to bu a meal of soup, bread and cookies and receive a beautiful handmade bowl. Musicians volunteer to pla for the dinner. For $12 the customers choose a bowl to keep and get the simple meal. For $8, ou get a simple meal, but no handmade bowl. Last ear, $96 was raised for charit. What are the possible combinations of meal-alone tickets and bowl-meal tickets that were sold at Empt Bowls? Let represent the number of bowl-meal tickets sold. Let represent the number of meal-alone tickets sold. An equation that models the situation is. 1. Answer the following questions based on the equation. a. What does the 12 mean? b. What does the 8 mean? Activit CT Algebra I Model Curriculum Version 3.

2 Name: Date: Page 2 of 6 c. The standard form of a linear equation is A +B = C. In, what number is: A B C d. Fill in the table that gives possible combinations for the numbers of bowl-meal tickets and the number of meal-alone tickets that might have been sold to raise $96. : # of Bowl-Meals tickets at $12 each : # of Meal Alone tickets at $8 each 6 3 e. Write ordered pairs and graph the points on a coordinate plane. Activit CT Algebra I Model Curriculum Version 3.

3 Name: Date: Page 3 of 6 f. What is the -intercept? What does it mean in the contet of the problem? g. What is the -intercept? What does it mean in the contet of the problem? h. What is the slope of the equation and what does it mean in the contet of the problem? i. Transform the equation = 96 into slope-intercept form ( ). Check to see that our answer in part (g) and (h) is the same slope and -intercept in part (i). 2. Graph the linear functions in standard form b finding the and intercepts. Then find the slope and write the equation in slope-intercept form. a. Given = 12, find both intercepts and the slope. Then draw the graph. -intercept: -intercept: Activit CT Algebra I Model Curriculum Version 3.

4 Name: Date: Page 4 of 6 Slope: b. Write = 12 in slope-intercept form: = m + b. c. From the slope-intercept form of the equation, the slope is and the -intercept is. Check to see that the results agree with our answers in part (a). d. Given 4 5 = 2, find both intercepts and the slope. Then draw the graph. -intercept: -intercept: Slope: e. Write 4 5 = 2 in slope-intercept form: = m + b. f. From the slope-intercept form of the equation, the slope is and the -intercept is. Check to see that the results agree with our answers in part (d). Activit CT Algebra I Model Curriculum Version 3.

5 Name: Date: Page 5 of 6 g. Given 6 5 = 3, find both intercepts and the slope. Then draw the graph. -intercept: -intercept: Slope: h. Write 6 5 = 3 in slope-intercept form: = m + b. 3. What is one advantage of the standard form (compared to slope-intercept form)? 4. What is one advantage of slope-intercept form? Activit CT Algebra I Model Curriculum Version 3.

6 Name: Date: Page 6 of 6 5. For its communit service this ear, the Lman Honor Societ has adopted the patients in the neighborhood Convalescent Home. The students visit the patients one afternoon a month to pla cards, chat, read aloud and write letters for patients. When Lebanon Florist learned about the Honor Societ s good deeds, the donated 36 stems of flowers and greens to the Honor Societ to bring cheer to the patients in the convalescent home. The students will make either a corsage for the women or a boutonniere for the men. Corsages will require 5 stems, and the boutonniere will require 3 stems. If the students use all 36 stems, what are the possible number of corsages and boutonnieres the can make? a. Choose a variable to represent the number of corsages the students can make. b. Choose a variable to represent the number of boutonnieres the students can make. c. Fill in 5 rows of a table that shows a specific number of boutonnieres depending on the number of corsages made. # of 5 stem corsages made 3 # of 3 stem boutonnieres d. Write a linear equation in standard form that models this situation. e. Write the equation from part (d) in slope-intercept form. Activit CT Algebra I Model Curriculum Version 3.

Investigating Intercepts

Investigating Intercepts Unit: 0 Lesson: 01 1. Can more than one line have the same slope? If more than one line has the same slope, what makes the lines different? a. Graph the following set of equations on the same set of aes.