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Algebraic Equations and Proportions Practice

This exercise focuses on finding slopes, solving equations, using ratios and proportions. It includes examples and a quiz to test understanding.

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Algebraic Equations and Proportions Practice

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  1. Warm Up Find the slope of the line through each pair of points. 1.(1, 5) and (3, 9) 2. (–6, 4) and (6, –2) Solve each equation. 3. 4x + 5x + 6x = 45 4. (x – 5)2 = 81 5. Write in simplest form. 2 x = 3 x = 14 or x = –4

  2. Notes 6-1 Proportions

  3. Ratios: • A ratio compares two numbers by division. • The ratio of two numbers a and b can be written as a to b, a:b, or , where b ≠ 0. • For example, the ratios 1 to 2, 1:2, and all represent the same comparison.

  4. Using Ratios in Figures: 90° 6 inches 8 inches 60° 30° 10 inches Ratio of the angles is 30:60:90 Ratio of the sides is 6:8:10 Simplified Ratio is 1:2:3 Simplified Ratio is 3:4:5

  5. Example: Using Ratios The ratio of the side lengths of a triangle is 4:7:5, and its perimeter is 96 cm. What are the lengths of the three sides? 24, 42, and 30 x = 6

  6. Example with angle measures: The ratio of the angle measures in a triangle is 1:6:13. What is the measure of each angle? x = 9° y = 54° z = 117°

  7. Proportions: • A proportion is an equation stating that two ratios are equal. • In the proportion , the values a and d are the extremes. • The values b and c are the means. • When the proportion is written as a:b = c:d, the extremes are in the first and last positions. The means are in the two middle positions.

  8. Solving Proportions

  9. Example Solve the proportion. d = 9

  10. Example: Solving Proportions Solve the proportion. z = 14 or z = –6

  11. Example Solve the proportion. x = 3 or x = –9

  12. Example Solve the proportion. y = 3 or y = –3

  13. Lesson Quiz 1. The ratio of the angle measures in a triangle is 1:5:6. What is the measure of each angle? Solve each proportion. 2.3. 4. Given that 14a = 35b, find the ratio of a to b in simplest form. 5. An apartment building is 90 ft tall and 55 ft wide. If a scale model of this building is 11 in. wide, how tall is the scale model of the building? 15°, 75°, 90° 3 7 or –7 18 in.

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