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Are You Ready? 6th Grade Pre-Algebra Chapter 8 Name: Date: ______ Block: ______ Vocabulary Write the definition of each term in your own words then write an appropriate example. 1) Relation: __________________________________________________________________ 2) Domain: __________________________________________________________________ 3) Range: __________________________________________________________________ 4) Function: __________________________________________________________________ 5) x-intercept: __________________________________________________________________ 6) y-intercept: __________________________________________________________________ 7) Slope: ____ __________________________________________________________________ 8) Slope intercept form: __________________________________________________________________ 9) Standard form: __________________________________________________________________ 10) Function notation: __________________________________________________________________ 11) Linear Equation: ______________________________________________________ __________________________________________________________________ 12) Solution of linear equations _____________________________________________ __________________________________________________________________ Skills 13) Identify the domain and range of the relation. (5, 2), (−1, 3), (3, −2), (−1, 3), (−4, 5) Domain: _______________________ Range: ______________________________ Represent the relation as a graph and as a mapping diagram. Then tell whether the relation is a function. Explain your reasoning. 14) (8, −5), (−6, 3), (5, 3), (8, −8), (4, 0) Function y Not a function Explain: x Tell whether the relation represented by the graph is a function. y Function 15) Not a function x Explain: _____ Tell whether the ordered pair is a solution of −𝟐𝒙 + 𝒚 = 𝟖. 16) (−2, 4) 17) (2, −4) __________ __________ 18) Let f(x) = 3x – 2 1 19) Let f(x) = - 4x + 3 Find f(x) when x = -1 Find x when f(x) = 1 y Graph the linear equations. 20) 𝑦 = −3𝑥 + 4 (𝑥, 𝑦) 𝑥 x y 1 21) 𝑦 = 4 𝑥 − 6 x Find the x and y intercepts of each equation then graph the equations. 22) 2𝑥 − 6𝑦 = 12 23) −𝑥 + 4𝑦 = 8 y y x x Find the slope of the line through the given points. 24) (2, –5), (6, 1) 25) (0, –3 )( 4, –7) y y x x 26) 27) Identify the slope and the y-intercept of the line with the given equations then graph each. y y 2 28) 𝑦 = − 5 𝑥 + 8 29) 𝑦 = 4𝑥 − 6 x x y y 30) 3𝑥 + 𝑦 = 7 31) −2𝑥 − 4𝑦 = 12 x x y y 32) 𝑥 = 3 33) 𝑦 = −6 x x Find the slope of a line parallel to the given line and the slope of a line perpendicular to the given line. 34) 35) 𝑦 = 2𝑥 − 6 Slope: _______ Slope: Parallel: _______ Parallel: Perpendicular: _______ 36) 3𝑥 + 6𝑦 = 18 _______ Slope: _______ _______ Parallel: _______ Perpendicular: _______ Perpendicular: _______ Write an equation of the line with the given information. 37) 1 38) slope = − 2 y − intercept = 3 slope = 5 y − intercept = −8 Write an equation in slope-intercept form that goes through the 2 given points. 39) 40) _______________________ _______________________ (3, 6) (0, 3) 41) (−1, −8) (0, 9) _______________________ Write an equation of the line that is parallel to the linear equation and goes through the given point. −2 42) 𝑦 = 4𝑥 + 3 ; (0, −6) 43) 𝑦 = 𝑥 − 2 ; (0, 3) 3 _______________________ _______________________ Write an equation of the line that is perpendicular to the linear equation and goes through the given point: 44) 𝑦 = 3𝑥 + 5 ; (0, −7) _______________________ 45) 𝑦= −4 5 𝑥 − 4 ; (0, 2) _______________________ 46) Tell whether (-1, 3) is a solution of the linear system: y = 5x -2 and y = -2x + 5. 47) Solve the linear system by graphing: 2x – 3y = 12 and x – y = 3 y x Applications 48) Suppose that after a volcanic eruption, lava from the volcano traveled 12 miles to a body of water at an average speed of 3 miles per hour. Write an equation to show the lava's distance 𝑦 (in miles) from the water 𝑥 hours after it left the volcano. a.) Make a table of solutions for the equation. 𝑥 (𝑥, 𝑦) b.) How long did it take the lava reach the water? c.) Explain what the ordered pair (2, 6) means. _________________________________________________________________ __________________________________________________________________________________________ You are in charge of buying food for a party. You have budgeted $54.00 for pizza and soda. A pack of soda costs $6.00 and one pizza costs $3.00. a) Write an equation describing the possible amounts of pizza and soda you can buy. b) Use intercepts to graph the equation. y 18 16 14 Pizzas 49) 12 10 8 6 c) If you buy 2 pizzas, how many packs of soda can you buy? 4 2 2 4 6 8 10 12 14 16 Packs of soda 18 x Writing Answer the following questions in complete sentences. Be sure to use examples and correct math terminology when possible. 50) Explain how to find the whether a point is a solution to a linear equation. 51) Describe 2 different strategies to graph a linear equation.