Alg2 S4 Summative Review Determine whether the relation is a function. (0, 4), (1, 4), (2, 5), (3, 6), (4, 6)

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1 Alg2 S4 Summative Review Determine whether the relation is a function (0, 4), (1, 4), (2, 5), (3, 6), (4, 6) 2 The boiling temperature of water T (in Fahrenheit) can be modeled by the function where a is the altitude of water (in feet) State and interpret the slope and y-intercept 7 Graph the linear equation by finding x- and y-intercepts 8 Find the slope and y-intercept of the graph of 3 Tell whether Line 1 and Line 2 are parallel, perpendicular, or neither Line 1 passes through (10, 7) and (13, 9) Line 2 passes through ( 4, 3) and ( 1, 5) 4 Which equation has the steeper graph, or? 5 Consider the line that passes through the points (4, 6) and (7, 6) a Find the equation of the line through the points (4, 6) and (7, 6) b Find the equation of the line perpendicular to the line in part (a) at the point (7, 6) Explain why the slopes are not negative reciprocals 6 A monthly phone bill, b, in dollars, consists of a $29 service fee plus $014 per minute, m, of long distance calls a Write a linear function to represent the bill as a function of minutes of long distance calls b Estimate the bill if 82 minutes of long distance calls are made 9 The road up Mount Culver is 45 miles long and rises an average of 140 feet per mile The road up Mount Winamac, which is 4800 feet tall, rises an average of 120 feet per mile Compare the heights of Mount Culver and Mount Winamac and the lengths of the roads up the mountains Explain your results 10 Which slope-intercept equation represents a line that passes through the point and is parallel to the line? a b c y = 1 4 x 5 d 11 Write the equation in standard form of the line that is perpendicular to the given line and passes through the given point ;

2 12 A rental car costs $25 plus a fixed charge per mile driven The total charge for 210 miles of use was $67 Write an equation for the cost, C (in dollars), in terms of the miles driven, x 17 Graph the inequality in a coordinate plane 13 A revenue of $1500 is obtained from the sales gift baskets at $50 each and movie passes at $25 each Write and graph an equation that shows the relationship between the numbers of items sold Determine 4 possible combinations of items sold 18 Graph the inequality in a coordinate plane 14 Write the standard form of the equation of the line that passes through the point and is parallel to the line 19 During a fish fry, 2-piece dinners and 4-piece dinners are sold There are up to 125 pieces of fish available for the dinners a Write an inequality for the number of fish dinners that can be sold using x as the number of 2-piece dinners and y as the number of 4-piece dinners b Graph the inequality you wrote in part (a) In which quadrant should your graph lie? Explain c Give 3 possible solutions to the inequality 15 Which of the following best describes the graphs of the equations below? a The lines are parallel b The lines are perpendicular c The lines have the same y-intercept d The lines have the same x-intercept 20 Tell whether the linear system has infinitely many solutions, one solution, or no solution If the system has infinitely many solutions, state three solutions to the system 16 Is the ordered pair ( 3, 7) a solution of the inequality?

3 21 Is (5, 2) a solution of the system? 2x + 6y = 2 x + 2y = 1 25 A group of 68 people attend a ball game There were three times as many children as adults in the group Write a system of equations that you could use to set up this problem, where a is the number of adults and c is the number of children in the group Solve the system of equations for c, the number of children in the group 22 The number of in-line skates sold between 1982 and 1991 can be modeled by the equation The number of roller skates sold during the same period can be modeled by, where x is the year Determine what year sales of in-line skates will exceed sales of roller skates 23 Solve the linear system 26 Write and graph a system of two linear equations with no solution 24 The Modern Grocery has cashews that sell for $475 a pound and peanuts that sell for $250 a pound How much of each must Albert, the grocer, mix to get 90 pounds of mixture that he can sell for $300 per pound Express the problem as a system of linear equations and solve using the method of your choice to find the solution of the problem 27 Suppose a sports club has a membership fee of $300 in addition to a $40 monthly fee while a gym has a membership fee of $400 but has a monthly fee of only $30 a Write a system of equations representing the cost of the club and the gym as a function of the number of months of use b Solve the system you wrote for part (a) What does the solution mean?

4 28 Graph the solution set to the system x 4 y 5 29 The Computer Club has a budget of at most $90 for a pizza party The club can get large pizzas for $10 and cases of soda for $350 The club would like to buy at least 5 large pizzas and at least 3 cases of soda a Write a system of linear inequalities that describes the given information b Graph the system you wrote in part (a) c Can the club buy 6 pizzas and 4 cases of soda? Explain d Find the maximum number of cases of soda the club can buy if the club decides to buy 7 pizzas 30 Solve the linear system

5 Alg2 S4 Summative Review Answer Section 1 It is a function 2 The slope is which indicates a decrease of temperature 0018 degrees F per foot Or maybe you prefer to say a decrease of 18 degrees F per 10,000 feet The y-intercept is 212 which would represent the boiling temp of water at altitude 0 feet That is, the boiling temp of water is 212 degrees F at sea level 3 parallel 4, because the slope is larger 5 I think it helps to graph the points and line to make the problem more clear y x a y = 6 b x = 7; Since the slope of the line y = 6 is 0, any line perpendicular to y = 6 has an undefined slope Therefore, the perpendicular line must be a vertical line such as x = 7 6 a bill=29+014minutes b=29+014m 7 b $ y x 10 8 ; y-intercept: 6

6 9 Since the road up Mount Culver rises an average of 140 feet per mile for 45 miles, Mount Culver must be = 6300 feet high So Mount Culver is 1500 feet higher than Mount Winamac The road up Mount Winamac is 10 B 11 = 40 miles long The road up Mount Winamac is 5 miles shorter than the road up Mount Culver The slope is -2 (y is movie passes over x is gift baskets) So I can trade in two movie passes for one gift basket, which makes good sense, because the gift basket costs twice as much (G,M): (0,60), (30,0), (10,40),(20,20) B 16 Yes y 10 x a

7 b See graph below The graph should lie in Quadrant I because the values of x and y must be non-negative c Sample answers: x = 10, y = 26; x = 20, y = 21; x = 30, y = infinitely many solutions 21 yes This equation is about the pounds: x + y = 90 This equation is about the value: 475x + 250y = 270 Solving by elimination or substitution works nicely x = 20 pounds of cashews y = 70 pounds of peanuts 25 Solve the linear system: by substitution: c = 3(17) = 51 children 26 Sample answer: x + y = 3 x + y = 1 27 a y = 40x + 300; y = 30x b The solution (10, 700) means that at 10 months the cost of the gym and the cost of the club are the same During the first 9 months, the sports club is cheaper; beginning with the 11th month, the gym is cheaper

8 28 29 a 10x + 35y 90 y 3 x 5 b c x = 6 and y = 4 is a solution of the system since 6 5, 4 3, and The point (6, 4) lies in the shaded region d Solve for y: so the club can afford to buy 5 cases of soda 30 no solution

1.3 LINEAR EQUATIONS IN TWO VARIABLES. Copyright Cengage Learning. All rights reserved.

1.3 LINEAR EQUATIONS IN TWO VARIABLES Copyright Cengage Learning. All rights reserved. What You Should Learn Use slope to graph linear equations in two variables. Find the slope of a line given two points