# 7th Gd, Jan. 17, Linear Functions

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7th Gd, Jan. 17, Linear Functions
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation?

Page in Workbook, 111, 1-6 Home Theater The number of home theaters a company sells varies directly as the money spent on advertising. How many home theaters does the company sell for each \$500 spent on advertising? Hint: If the company spends \$1000 on advertising, they will sell 16 home theaters. \$500/\$1000 is ½, so what is ½ of 16?

Ordered pairs are: (50,4) and (75,6) Y2-Y1/ X2-X1 6-4/75-50 = 2/25
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation? Dune Buggy Beach Travel rents dune buggies for \$50 for 4 hours or \$75 for 6 hours. What is the hourly rate? Ordered pairs are: (50,4) and (75,6) Y2-Y1/ X2-X1 6-4/75-50 = 2/25 Hourly rate =

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation? 3. Fertilizer Leroy uses 20 lbs. of fertilizer to cover 4,000 square feet of his lawn and 50 lbs. to cover 10,000 sq. ft. How much does he need to cover his entire yard which has an area of 26,400 sq. ft.? Ordered pairs are: (20, 4,000), (50, 10,000) and (X, 26,400) Y2-Y1/X2-X1= 10,000-4,000/50-20= 6,000/30=200 Slope or k is 200 y/x=k 26,400/x=200 26,400/x=200/1 200x=26,400 X=26,400/200 X= lbs of fertilizer to cover his entire yard

Miles/Gallons> 180/6= ; 240/8=
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation? Determine whether this linear function is a direct variation. If so, state the constant of variation (CV). Miles/Gallons> 180/6= ; 240/8= 300/10= ; 360/12= Are the ratios the same ( a direct variation)? If so, what is the CV? Gallons,X 6 8 10 12 Miles, y 180 240 300 360

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation? 5. Is this linear function a direct variation? If so, what is the constant of variation (CV)? Temp.y/Time (min.)X > 82/10= ; 83/11= 84/12= ; 85/13= Is this a direct variation? What is the CV? Time/min.X 10 11 12 13 Temp. (y) 82 83 84 85

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests a directly proportional or linear relationship. Essential Questions: How do I read a graph of a relationship that is proportional or linear? How do I determine whether a linear function is a direct variation? 6. Is this linear function a direct variation? If so, what is the constant of variation (CV)? 1,500/6= ; 2,750/11= ; 4,000/16= 5,250/21= Is this function a direct variation? If so, what is the CV? Number of Payments,X 6 11 16 21 Amount Paid, y 1,500 2.750 4,000 5,250

Essential Question: How do I write an equation for the direct variation; how do I find the value ?
7. If y = -4 when x = 10, find y when x = 5 y/x=k -4/10=k -2/5=k Y/x= k Y/x=-2/5 Y= y/x = y/x -4/10 = y/5 Cross multiply then divide to find the value

Essential Question: How do I write an equation for the direct variation; how do I find the value ?
8. If y = 12 when x = -15, find y when x = 2 y/x=k 12/-15=-.8 Y/x=-.8 Y= y/x = y/x 12/15 = y/2 Cross multiply then divide

Essential Question: How do I write an equation for the direct variation; how do I find the value ?
9. Find x when y = 18, if y = 9 when x = 8. Write an equation using the same process as in #7 and #8 y/x = y/x 18/x = 9/ 8 Cross multiply then divide

Inverse Variation, Workbook, p. 113, Tues.Jan.12
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Question: How do I determine if a graph of a relationship is an inverse variation? Inverse Variation, Workbook, p. 113, Tues.Jan.12 Ocean This table shows the relationship between the temperature of the ocean and its depth. Graph the data in the table and determine if the relationship is an inverse variation. Temp.(C)D 4 8 40 50 Dept. (m) 1.000 500 100 80

1. Ocean: After you graph, determine if the relationship is an inverse variation. Remember- In an inverse variation, X multiplied by Y is the same in all ordered pairs and the line will not be straight.

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Question: How do I determine if a graph of a relationship is an inverse variation? 2. Conduit The table shows the relationship between the velocity of a fluid flowing in a conduit and the area of a cross section of the conduit. Graph the data in the table and determine if the relationship is an inverse variation (hint: the line will not be straight). Velocity (ft/s) 25 50 100 Area (in.squared) 2 1 1/2

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Question: How do I determine if a graph of a relationship is an inverse variation? 2. Conduit Is it an inverse variation? 4.00 3 2 1 50 100

Cups Ordered 10,000 7,500 6,000 Cost/100 cups (\$) 3 4 5
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Question: How do I determine if a graph of a relationship is an inverse variation? 3. Paper Cups The table shows the relationship between the number of paper cups ordered and the cost per 100 cups. Graph the data in the table and determine if the relationship is an inverse variation. Cups Ordered 10,000 7,500 6,000 Cost/100 cups (\$) 3 4 5

3. Paper Cups GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Question: How do I determine if a graph of a relationship is an inverse variation? Is this completed graph an inverse variation? 4.00 3 2 1 5,000 10,000

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Questions: How do I determine if a graph of a relationship is an inverse variation? 4. Wages Mr. Anschutz’s annual salary is shown in the table. Graph the data in the table and determine if the relationship is an inverse variation. Year 2002 2005 2008 2011 Salary (\$) 34,000 38,000 42,000 46,000

GLE 0706. 3. 5 Understand and graph proportional relationships
GLE Understand and graph proportional relationships. SPI Recognize whether information given in a table, graph, or formula suggests an inverse variation. Essential Questions: How do I determine if a graph of a relationship is an inverse variation? Is the completed graph for #4 below an inverse variation? 42,000 38,000 34,000 30,000 2002 2005 2008 2011