Main Idea and New Vocabulary Example 1: Real-World Example: Translate a Table into an Equation Example 2: Real-World Example: Translate a Table into an Equation Example 3: Real-World Example: Translate a Graph into an Equation Example 4: Real-World Example: Translate a Graph into an Equation Key Concept: Representing Equations Example 5: Real-World Example: Represent Equations Example 6: Real-World Example: Represent Equations Lesson Menu

Translate tables and graphs into linear equations. Main Idea/Vocabulary

Translate a Table into an Equation MEASUREMENT The table shows the relationship between miles and kilometers. Write an equation to find the number of miles in any number of kilometers. Describe the relationship in words. Example 1

Translate a Table into an Equation Let k represent the kilometers and m represent the miles. Answer: The equation is m = 0.62k. There is 0.62 mile in every kilometer. Example 1

The table shows the relationship between kilograms and pounds The table shows the relationship between kilograms and pounds. Write an equation to find the number of kilograms in any number of pounds. A. k = 0.45p B. p = 0.45k C. p = 0.45 + k D. k = 1 – 0.55p Example 1 CYP

Translate a Table into an Equation MEASUREMENT The table shows the relationship between miles and kilometers. Use the equation m = 0.62k to find the number of miles in 20 kilometers. m = 0.62k Write the equation. m = 0.62(20) Replace k with 20. m = 12.4 Multiply. Answer: There are 12.4 miles in 20 kilometers. Example 2

The table shows the relationship between kilograms and pounds The table shows the relationship between kilograms and pounds. Use the equation k = 0.45p to find the number of kilograms in 9 pounds. A. 3.75 kilograms B. 3.6 kilograms C. 4.05 kilograms D. 4.5 kilograms Example 2 CYP

Translate a Graph into an Equation HIKING The total numbers of miles Suki hiked on certain days are shown. Write an equation to find the number of miles hiked after any number of days. The ordered pairs shown on the graph are (1, 1.5), (2, 3), (3, 4.5), (4, 6), and (5, 7.5). Example 3

Translate a Graph into an Equation Let m represent the miles and d represent the days. Answer: The equation is m = 1.5d. Example 3

BICYCLING The total numbers of miles Robert bicycled on certain days are shown. Write an equation to find the number of miles m biked after any number of days d. A. m = 4.5d B. m = 5.5d C. d = 4.5m D. d = 5.5m Example 3 CYP

Translate a Graph into an Equation HIKING The total numbers of miles Suki hiked on certain days are shown. Use the equation m = 1.5d to find the number of miles Suki will hike after 1 week. Example 4

Translate a Graph into an Equation m = 1.5d Write the equation. m = 1.5(7) Replace d with 7. m = 10.5 Multiply. Answer: Suki will hike 10.5 miles after 1 week. Example 4

BICYCLING The total numbers of miles Robert bicycled on certain days are shown. Use the equation m = 4.5d to find the number of miles Robert will ride after 2 weeks. A. 31.5 miles B. 54 miles C. 63 miles D. 67 miles Example 4 CYP

Key Concept

Let b represent the number of beats and m represent the minutes. Represent Equations HEART RATES The average heart rate of a chicken is 275 beats per minute. Write an equation to find the number of beats in any number of minutes. Let b represent the number of beats and m represent the minutes. Answer: The equation is b = 275m. Example 5

MUSIC The tempo of a song is measured in beats per minute MUSIC The tempo of a song is measured in beats per minute. If a song’s tempo is 120 beats per minute, write an equation to find the number of beats b in any number of minutes m. A. m = 120b B. m = 60b C. b = 120m D. b = 60m Example 5 CYP

Represent Equations HEART RATES The average heart rate of a chicken is 275 beats per minute. Make a table to find the number of beats in 1, 2, 3, 4, or 5 minutes. Then graph the ordered pairs. Answer: Example 6

MUSIC The tempo of a song is measured in beats per minute MUSIC The tempo of a song is measured in beats per minute. If a song’s tempo is 120 beats per minute, make a table to find the number of beats in 1, 2, 3, or 4 minutes. A. B. C. D. Example 6 CYP