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Answers to Study Guide for “Moving Straight Ahead” 1. Given one of the representations below, find the other two. Table Graph (each box is 1 unit per side) Equation i. ii. y= x+1 iii. a. Find the y-intercept for each representation above. i. __________ ii.____________ iii._____________ b. Find the slope for each representation above. i. _________ ii. ____________ Answer: Table iii. ______________ Graph Equation y = –3x + 8 y = 4x – 3 y= x+1 2. Gretchen was absent when the class developed strategies for solving linear equations. Write an explanation to her about how to solve equations. Use the equation 4n – 17 = 43 as an example. Answer: You can think of solving an equation like this one as reversing the procedure that was done to create the expression on the left. To make 4n – 17 you would multiply n by 4 and then subtract 17. To reverse this, you add 17, then divide by 4. 3. a.This table shows two points that are on the same straight line. Complete the table to show three other points on the same line. Answer: x -3 -2 -1 0 1 y -2 0 2 4 6 b. Find the slope and the y-intercept of this line that represents the data. Write the equation. slope , y-intercept ; equation: y = 2x + 4 4. Here is a graph of three lines. a. Complete the chart. line constant rate of change (slope) y-intercept A B C b. Here are the equations of the three lines. Match each line with its equation. , , line A: ____________, line B: ____________, line C: ____________ Answer: The equation for the line labeled A: y = 3 – x; the equation for the line labeled B: y = 2 + x; the equation for the line labeled C: y = – 4 + 2x a. line A B C b. line A: y = 3 – x, constant rate of change –1 1 2 y-intercept (0, 3) (0, 2) (0, –4) line B: y = 2 + x, line C: y = –4 + 2x 5. The equations below represent the costs to print brochures at three different printers. a. For which equation does the point (20, 60) lie on the graph? Explain. i. C = $15 + $2.50N ii. C = $50 + $1.75N iii. C = $30 + $1.50N Answer: a. Equation iii because the point satisfies the equation: 60 = 30 + 1.5(20). 6. Find the number described in each problem by writing and solving an equation. a. If Sarah subtracts five times her number from 24, she gets 4. What is Sarah's number? Answer: a. 24 – 5x = 4; 4 c. The sum of 4 times a number and 4 is 16. What is the number? Answer: 4x + 4 = 16; 3 7. Solve the following equations for the value of x: a. 3x + 5 = 4x – 10 b. 4x + 10 = 6x – 8 a. x = 15 b. c. 3x + 10 = 5x d. 3x – 11 = 8x – 21 c. x = 5 d. x=9 x=2 e. 3(x + 8) = 12 e. x = –4 8. Find the slope and y-intercept of the line represented by each equation. a. y = 7x + 1 slope is 7; y-intercept is (0, 1) c. y = 4x slope is 4; y-intercept is (0,0) b. y = 5 - 2x slope is –2; y-intercept is (0, 5) d. y = -3x – 8 slope is –3; y=intercept is (0, -8)