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Algebra 1: Word Problems with direct and inverse variations 3/15/16 WARM UP 1. Write out all the equations related with direct and inverse variation. Direct Inverse Equation 1: _____________________ _________________________ Equation 2: _____________________ _________________________ Equation 3: _____________________ _________________________ 2. Identify the following as direct variation, inverse variation, or neither. (a) (c) (e) answer: _____________ answer: _______________ answer: ____________ (b) answer: _____________ (d) answer: _______________ (f) (3, 2), (6, 1), answer: _______ ____ 3. Which tables below represents a direct variation table? a c b d CLASS WORK/HOMEWORK 4. Plot 3 more points on the graph below to create a direct variation graph. 5. H varies inversely as J. When J = -4, H = 9. Find J when H = 6. answer: ________________________ ____ ____ ____ 6. If T varies directly as W. When T = -6, W = 12. What is the value of W when T = 8? a -16 b 12 c 6 d -8 7. A varies inversely as B. When A = 18, B = 4. Find B when A = 9. a 8 c b 12 d 8. A relationship exists between the distance, d (in miles) a car can cover and the number of gallons og gas, g, it consumes. * A car covering a distance of 105 miles consumes 3 gallons of gas. * A car covering a distance of 280 miles consumes 8 gallons of gas * Let d represents the distance in miles. * Let g represents the gallons of gas consume. Which statement is true about this relationship? a The distance varies inversely with the gallons of gas consumed because . The distance varies directly with the gallons of gas consumed because . c The distance varies inversely with the gallons of gas consumed because . d The distance varies directly with the gallons of gas consumed because b . 9. The width of a box varies directly with its length. If the length is 18 inches, the width is 6 inches. What is the length of a box with a width of 24 inches? answer: _________ 10. (a) Graph 11. (b) ____ 12. Which expression(s) below is/are modeled by the algebra tiles above? a c b d 13. Write the equation of the line passing through the points (-4, -5) and (4,1). slope-intercet form: ___________________ 14. Graph by finding x-intercept and y-intercept. x-intercept = _________ ____ 15. y-intercept = ________ What is the equation of the graph below? a b ____ 16. A line has a slope of c d and passes through the point line? (MORE THAN ONE ANSWER) a (3, -10) c (2, -2) b (2, ) d (0, -3) . Which of the following points lie on the ____ 17. Which line(s) is/are parallel to ? a b c d 8y=-4x-16 ____ 18. Which line below is perpendicular to ? a b c d 19. Which choices below is true for ? (MORE THAN ONE ANSWER) ____ 20. A vertical line passes through the point (4, -7). What is the equation of this line? a x = -7 c y = -7 b x=4 d y=4 21. Graph y = -4: the slope is ________________. ____ 22. A function h(x) is described as . * the domain of h(x) is all real numbers greater than 0. * The range of h(x) is all real numbers less than or equal to ____________ . a 3 b -2 23. Write equations for the given graph equation 1: __________________ equation 2: __________________ c -1 d 5