7.3 Lecture

Section 7.3 Spring 2023 Using Slope to Graph Equations of Lines and Linear Models The average cost of a Christmas tree in the United States, c , between the years 2012 and 2022 is modeled by the equation c = 5 t + 30 , where t is measured in years since 2010. 1. Identify the slope. Interpret your results. The slope is 5. The cost of a Christmas tree is increasing by $5 per year. 2. Identify the c- intercept. Interpret your results. The c-intercept is 30. In 2010, the starting cost for Christmas trees is $30. 3. Identify the t- intercept. Interpret your results. 0 = 5 t + 30 ,so theintercept is − 6. In 2004 the cost of a Christmas tree was $0. 4. Sketch a graph of the linear model. m = 5 1 = 5 up 1 ¿ ¿ = 5 down 1 ¿ = − 5 − 1 ¿ c = 5 ( 4 ) + 30 = 50 5. Estimate the cost of a Christmas tree in 2020. What kind of prediction did you make? 2020- 2010= 10 = t c = 5 ( 10 ) + 30 = 50 + 30 = 80 The cost of a Christmas tree in 2020 was $80.

Part-time students at UA paid tuition according to the graph below for spring 2023. 6. Find the equation for the linear model for part-time tuition at UA in spring 2023. y = 937 x + 34 m = y 2 − y 1 x 2 − x 1 = 3782 − 34 4 − 0 = 3748 4 = 937 7. Use your model to predict the tuition for 8 credit hours. y = 937 ( 8 ) + 34 = 7496 + 34 = 7530 It would cost $7,530 to take 8 credit hours. 8. Use your model to predict the number of credit hours that can be taken for $2000. 2000 = 937 x + 34 1966 = 937 x x = 2.1 Find the slope and the y -intercept for each graph. 9. slope = 2/3 y -intercept = -2 0 1 2 3 4 5 0 500 1000 1500 2000 2500 3000 3500 4000 34 3782 Part-Time Tuition Cost Number of Credit Hours Cost (in dollars)