Since Colleen is assuming that the chick grows linearly, the equation will be in the form y = mx + b. Without graphing, what do m and b represent? Do you know either of these values? If so, what are their units? You already know the chicken’s rate of growth. Place this into the equation of the line. What information is still unknown? In Lesson 2.1.4, you discovered that knowing the slope and a point is enough information to determine a line. Therefore, using the point (9, 98.4) should help you find the How can you use this point in your equation? Discuss this with your team and be ready to share your ideas with the rest of the class. Work together as a class to solve for b (the weight of the chick when it was hatched). Write the equation of the line that represents the weight of the chick. Does the y-intercept you found algebraically match the one you found using the graph? Does it match the one you found using the table? How accurate do you think your algebraic answer is? What are the units for the y-intercept? Use your equation to determine when Colleen’s chicken will weigh 140 grams. 2-79. Use this new algebraic method to find equations for lines with the following properties: A slope of −3, passing through the point (15, −50). A slope of 0.5 with an x-intercept of (28, 0) 2-80. MIGHTY MT. EVEREST The Earth’s surface is composed of gigantic plates that are constantly moving. Currently, India lies on a plate that is slowly drifting northward. India’s plate is grinding into the rest of Asia. As it does so, it pushes up the Himalayan Mountains, which contain the world’s highest peak, Mt. Everest. In 1999, mountain climbers measured Mt. Everest with satellite gear and found it to be 8850 meters high. Geologists estimate that Mt. Everest may be growing by as much as 5 cm per year. Your Task: Assuming a constant growth of 5 cm per year, determine how tall Mt. Everest was in the year 0. (The year 0 is the year that came 2000 years before the year 2000.) Write an equation for the height of Mt. Everest over time, with x representing the year and y representing the height of the mountain. What are the units for m and b in your equation? How many decimal places should be in your answer? Explain why.
The slope is 5.2, so y = 5.2x + b. The y-intercept is still unknown. Possible response: A point on a line is a solution to the equation, so when substituting the x- and y-values into the equation, the equation is still true. Substituting y = 9 and y = 98.4 into the equation, the equation becomes 98.4 = 5.2(9) + b. After solving, b = 51.6 and y = 5.2x + 51.6. The equation is exact and the units for the y-intercept are grams. Starting with 140 = 5.2x + 51.6, the solution becomes x = 17 days. 2-79. See below: y = –3x – 5 y = 0.5x – 14 2-80. Mt. Everest was 8750.05 meters tall in the year 0; y = 0.05x + 8750.05. The units for m are years and for b are meters. The answer should be carried to the hundredths place because 5 cm is .05 m. 2-81. See Suggested Lesson Activity for possible answers. 2-82. See below: y = 1.5x + 0.5 Answers vary, but solutions should lie on y = 1.5x + 0.5. Possible points: (0, 0.5), (1, 2), (10, 15.5) 2-83. Find solutions in bold in the diamonds below: 2-84. See below: (3.5, 0) and (0, –2.33) y = ≈ 4.33 2-85. See below: 3, (0, 5) , (0, 0) 0, (0, 3) 4, (0, 7) 2-86. See graph below: