Name: ate: 1 The table shows the cost of a vacation package for a given number of people. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation. People ost ($) 2 90 3 135 4 180 5 225 dollars per person; the cost is $45 for each person. dollars per person; the cost is $1 for 225 people. dollars per room; the cost is $45 for each person. dollars per person; the cost is $90 for each person. opyright 2005-2006 by Pearson Education Page 1 of 9
2 The table shows the number of miles driven over time. The rate of change is constant in the table. Find the rate of change. Explain what the rate of change means for the situation. Time (hours) istance (miles) 4 208 6 312 8 416 10 520 10; your car travels for 10 hours. ; your car travels 52 miles every 1 hour. 208; your car travels 208 miles. ; your car travels 52 miles every 1 hour. 3 Find the slope of the line passing through the pair of points. (7, 6) and ( 7, 6) 1 4 Find the slope of the line passing through the pair of points. ( 4, 5) and (0, 2) undefined opyright 2005-2006 by Pearson Education Page 2 of 9
5 Find the slope of the line passing through the pair of points. ( 2, 3) and ( 2, 7) 4 0 undefined 6 Find the slope of the line passing through the pair of points. ( 4, 5) and (5, 4) 1 1 9 9 7 Is the equation a direct variation? If it is, find the constant of variation. y = 2x yes; 2 yes; 1 yes; 0 no 8 Is the equation a direct variation? If it is, find the constant of variation. y = x 2 yes; 2 yes; 1 yes; 0 no opyright 2005-2006 by Pearson Education Page 3 of 9
9 Is the equation a direct variation? If it is, find the constant of variation. yes; 3 yes; 0 no 10 Find the slope and y-intercept of the graph of the equation. y = 6.5x + 4.7 The slope is 6.5 and the y-intercept is 4.7. The slope is 4.7 and the y-intercept is 6.5. The slope is 4.7 and the y-intercept is 6.5. The slope is 6.5 and the y-intercept is 4.7. 11 Find the slope and y-intercept of the graph of the equation. The slope is and the y-intercept is. The slope is and the y-intercept is. The slope is and the y-intercept is. The slope is 2 and the y-intercept is. 12 In 1990, people in the United States spent $52.9 billion on video and audio products. In 2000, people spent $106.9 billion on video and audio products. What was the rate of change? $54 billion per year $5.4 billion per year $540 billion per year $54 million per year opyright 2005-2006 by Pearson Education Page 4 of 9
13 The circumference of a circle varies directly with its radius. circle with a radius of 4 has a circumference of about 25.1 in. 2. What would be the circumference of a circle with a radius of 9 in.? about 34.1 in. 2 about 125.6 in. 2 about 56.5 in. 2 about 226.1 in. 2 14 Write the slope-intercept form of the equation for the line. y = 2x 1 y = 2x 1 15 Write the slope-intercept form of the equation for the line. y = 4x + 12 y = 4x + 12 opyright 2005-2006 by Pearson Education Page 5 of 9
16 Graph the equation. y = 2x 4 opyright 2005-2006 by Pearson Education Page 6 of 9
17 Graph the equation. 18 Write an equation in point-slope form for the line through the given point with the given slope. opyright 2005-2006 by Pearson Education Page 7 of 9
19 Write an equation in point-slope form for the line through the given point with the given slope. (0, 3); m = 18 y 3 = 18x y 3 = 18x y + 3 = 18x y + 3 = 18x 20 Write an equation for the line in point slope form through the points (2, 6) and ( 1, 8). 21 Use the point-slope form to write an equation of a line through the given points. ( 3, 2) and (3, 4) y 3 = x + 2 22 Suppose you are given a graph of a linear equation. ompare the methods you would use to find the equation of the line in slope-intercept form and in point-slope form. To find either equation, find the slope and y-intercept of the line as well as the coordinates of one point on the line. ll of these can be found from the graph. To find either equation, find the y-intercept of the line. For slope-intercept form, find the slope from the graph. For point-slope form, find the coordinates of one point on the line, which can also be read from the graph. To find either equation, find the coordinates of one point on the line. For slopeintercept form, find the y-intercept from the graph. For point-slope form, find the slope of the line. To find either equation, find the slope of the line. For slope-intercept form, find the y-intercept from the graph. For point-slope form, find the coordinates of one point on the line, which can also be read from the graph. opyright 2005-2006 by Pearson Education Page 8 of 9
23 How can you find the x-intercept of the graph of a linear equation? Substitute x = 0 into the equation and solve for y. Substitute y = 0 into the equation and solve for x. Substitute x = 1 into the equation and solve for x. Substitute y = 1 into the equation and solve for y. 24 an you graph a line if its slope is 0? Explain. Yes, the graph of a line with a slope of 0 is a horizontal line. Yes, the graph of a line with a slope of 0 is a vertical line. Yes, the graph of a line with a slope of 0 is a diagonal line. No, a slope of 0 does not exist, so the line cannot be graphed. 25 car company offers financing to its customers. For the newest model, customers can pay $2000 down and then $250 a month. Write an equation for this situation. What does the independent variable represent? What does the dependent variable represent? y = 250x + 2000; the independent variable, x, represents the amount of money paid on the car and the dependent variable, y, represents the number of months after buying the car. y = 2000x + 250; the independent variable, x, represents the amount of money paid on the car and the dependent variable, y, represents the number of months after buying the car. y = 250x + 2000; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car. y = 2000x + 250; the independent variable, x, represents the number of months after buying the car and the dependent variable, y, represents the amount of money paid on the car. opyright 2005-2006 by Pearson Education Page 9 of 9