Practice A Graphing Linear Equations

Transcription

1 1-1 Practice A Graphing Linear Equations Complete the tables for the given equations (, ) 3 3( 3) 7 ( 3, 7) 3() (, ) 1 3( 1) 1 ( 1, 1) 0 3(0) (0, ) 1 3(1) 5 (1, 5) 3() (, ) 3 3(3) 11 (3, 11) 3 (, ) 3 ( 3) 3 0 ( 3, 0) () 3 1 (, 1) 1 ( 1) 3 ( 1, ) 0 (0) 3 3 (0, 3) 1 (1) 3 (1, ) () 3 5 (, 5) 3 (3) 3 6 (3, 6) Complete the table for the given equation. Then graph the equation (, ) 3 ( 3) 1 7 ( 3, 7) () 1 5 (, 5) 1 ( 1) 1 3 ( 1, 3) 0 (0) 1 1 (0, 1) 1 (1) 1 1 (1, 1) () 1 3 (, 3) 3 (3) 1 5 (3, 5) O. Is the equation in Eercise 3 linear? Eplain. Possible answer: 1 unit, units. Copright b Holt, Rinehart and Winston. 3 Holt Mathematics

2 1-1 Practice B Graphing Linear Equations Graph each equation and tell whether it is linear O O O O 5. A real estate agent commission ma be based on the equation C 0.06s 50, where s represents the total sales. If the agent sells a propert for $15,000, what is the commission earned b the agent? Graph the equation and tell whether it is linear O (thousands) Copright b Holt, Rinehart and Winston. Holt Mathematics

3 1- Practice A Slope of a Line Find the slope of the line that passes through each pair of points. 1. (1, 0), (, ). (6, ), (, ) 3. ( 1, 1), (, ) ( 7, ), (, 1) 5. (5, 3), (, 3) 6. ( 3, ), (, 7) Determine whether each graph shows a constant or variable rate of change. Eplain our reasoning. 7.. O O constant; The slo t the same. variable; The saries from point tooint. 9.. O O variable; The sle varies from oint. constant; The sloe between an s the same. Copright b Holt, Rinehart and Winston. 1 Holt Mathematics

4 1- Practice B Slope of a Line Find the slope of the line that passes through each pair of points. 1. (, ), (1, ). (, 0), (0, ), 3. (0, ), (, ). (3, 6), (, ) 0 5. ( 3, ), (3, ) 6. (3, 0), (0, 6), 7. (3, ), (3, ). (, ), (3, 1) 3 undefined 5 7 Determine whether each graph shows a constant or variable rate of change. Eplain our reasoning O O O constant; The sloe between anints is alwa the same. constant; The s between aoints is alw the same. variable; The sle is and negative in Quadrant IV. 1. The table shows the distance Ms. Long had traveled as she went to the beach. Use the data to make a graph. Find the slope of the line and eplain what it shows. The slope is 3, which means that for ever drivhe travels 3 miles. 0 Time (min) Distance (mi) Distance Traveled (mi) She is drih. Miles Time (min) 0 Copright b Holt, Rinehart and Winston. 13 Holt Mathematics

5 11-3 Practice A Using Slopes and Intercepts 1. Name the ordered pair if the -intercept is.. Name the ordered pair if the -intercept is. 3. In the ordered pair (9, 0), what is the -intercept?. In the ordered pair (0, 0), what is the relationship of the -intercept and -intercept? Find the -intercept and -intercept of each line. Use the intercepts to graph the equation O O -intercet is 5; m ; b 5 -intercis 3; m ; b 5 Write each equation in slope-intercept form, and then find the slope and -intercept m ; b 5 m ; b 5 m ; b 5 m 1; b 1 ; m 1 ; b Write the equation of the line that passes through each pair of points in slope-intercept form.. (1, ), ( 1, 0) 11. (1, 3), ( 1, 1) 1. (1, 1), ( 3, 3) Copright b Holt, Rinehart and Winston. 1 Holt Mathematics

6 1-3 Practice B Using Slopes and Intercepts Find the -intercept and -intercept of each line. Use the intercepts to graph the equation O O -interct is 3; -interct is 3; -interct is 3; -interct is 3; Write each equation in slope-intercept form, and then find the slope and -intercept b 0 b 0 b 0 b 15 b 0 b Write the equation of the line that passes through each pair of points in slope-intercept form. 6. (3, ), (, 6) 7. ( 1, 1), (, ). (6, 5), ( 9, 0) b 0 9. Apizzeria charges $ for a large cheese pizza, plus $ for each topping. The total cost for a large pizza is given b the equation C t, where t is the number of toppings. Identif the slope and -intercept, and use them to graph the equation for t between 0 and 5 toppings. The slt is. b 0 b 0 Copright b Holt, Rinehart and Winston. Holt Mathematics Dollars 0 Cost of Large Pizza 5 Number of Toppings

7 1- Practice A Point-Slope Form Use the point-slope form of each equation to identif the slope of the line ( 3). 1( 7) ( ) m m 1 m 3 Use the point-slope form of each equation to identif a point each line passes through.. 1 ( ) ( 1) 6. 5 ( 6) ( 1, 1 ) (, 1) ( 1, 1 ) (1, 3) ( 1, 1 ) ( 6, 5) Use the point-slope form of each equation to identif a point the line passes through and the slope of the line ( 3). 6 3( 1) ( ) m ; ( 1, 1 ) (3, 9) m 3; ( 1, 1 ) (1, 6) m 7; ( 1, 1 ) (, 1). 6( 7) ( 9) ( 9) m 6; ( 1, 1 ) (7, ) m 5; ( 1, 1 ) ( 9, 6) m 1 3 ; ( 1, 1 ) ( 9, 3) Write the point-slope form of the equation with the given slope that passes through the indicated point. 13. the line with slope passing though (5, ) 1. the line with slope passing through ( 1, ) Copright b Holt, Rinehart and Winston. 30 Holt Mathematics

8 1- Practice B Point-Slope Form Use the point-slope form of each equation to identif a point the line passes through and the slope of the line. 1. ( 1). 1 ( 3) 3. 3( 1) m ; ( 1, 1 ) (1, ) m ; ( 1, 1 ) (3, 1) m 3; ( 1, 1 ) ( 1, ). 5 ( 6) 5. 9( 3) ( 7) m ; ( 1, 1 ) ( 6, 5) m 9; ( 1, 1 ) ( 3, ) m 7; ( 1, 1 ) (7, 7) 7. 6( ). 1.5( ) 9. 1 ( 3) m 6; ( 1, 1 ) (, ) m.5; ( 1, 1 ) (, 1) m 1 ; ( 1, 1 ) (3, ) Write the point-slope form of the equation with the given slope that passes through the indicated point.. the line with slope 1 passing through (, 5) the line with slope passing through ( 3, ) 11. the line with slope passing through ( 1, ) 13. the line with slope 3 passing through (7, 6) 1. the line with slope 3 passing through ( 6, ) 3( 6) 15. the line with slope passing through (5, 1) 16. Michael was driving at a constant speed of 60 mph when he crossed the Sand River. After 1 hour, he passed a highwa marker for mile. Write an equation in point-slope form, and find which highwa marker he will pass 90 minutes after crossing the Sand River. arker for 11 miles Copright b Holt, Rinehart and Winston. 31 Holt Mathematics

9 1-5 Practice A Direct Variation The following tables show direct variation for the given equation. Complete the missing information in the tables Make a graph to determine whether the data sets show direct variation O The data sets show direct variation. Find each equation of direct variation, given that varies directl with.. is when is. 5. is when is is 50 when is is 15 when is At a constant speed, the gasoline a car uses varies directl with the distance the car travels. A car uses gallons of gasoline to travel miles. How man gallons will the car use to travel 9 miles? 5 Copright b Holt, Rinehart and Winston. 3 Holt Mathematics

10 1-5 Practice B Direct Variation Make a graph to determine whether the data sets show direct variation The data sets show direct variation.. Write the equation of direct variation for Eercise or O Find each equation of direct variation, given that varies with. 3. is 3 when is 5. is 63 when is is 7.5 when is is when is is 0 when is is 90 when is The table shows the length and width of various U.S. flags. Determine whether there is direct variation between the two data sets. If so, find the equation of direct variation. There is direct variation between the les. 1.9, where h, is the width, and 1.9 is the constant o Length (ft) Width (ft) Copright b Holt, Rinehart and Winston. 39 Holt Mathematics

11 1-6 Practice A Graphing Inequalities in Two Variables 1. The graph shows.. The graph shows. Shade Shade the the inequalit the side of the line to show the. inequalit. O O Solve each inequalit for Graph each inequalit O O 9. Georgia has scored at least 1 points in each of her basketball games this ear. She has scored both -point and 3-point field goals in ever game. Let equal the -point shots and equal the 3-point shots. Write and graph an inequalit to show the number of points she scored each game. 3 1, or 3 6 O 6 Copright b Holt, Rinehart and Winston. 6 Holt Mathematics

12 1-6 Practice B Graphing Inequalities in Two Variables Graph each inequalit O O 3. (3 ) O O 5. a. Atheater club hopes to raise at least $550 on the opening night of its new show. Student tickets for the show cost $.75, and adult tickets cost $5.50. Write and graph an inequalit showing the numbers of tickets that would meet the club s goal , or b. If the club sells 95 student tickets and 0 adult tickets, will it meet its goal? no Copright b Holt, Rinehart and Winston. 7 Holt Mathematics

13 1-7 Practice A Lines of Best Fit Find the mean of the - and -coordinates of each set of data m.5; m m 9; m Plot the data points for Eercise 1.. Plot the data points for Eercise Draw a line through ( m, m ) of 6. Draw a line through ( m, m ) of Eercise 3 to best fit the data. Eercise to best fit the data. Possible answer is shown above. Possible answer is shown above. 7. Write the equation of the line of best fit for Eercise Write the equation of the line of best fit for Eercise Copright b Holt, Rinehart and Winston. 55 Holt Mathematics

14 1-7 Practice B Lines of Best Fit Plot the data and find a line of best fit Find the line of best fit for the student enrollment data. Use the equation of the line to predict what the enrollment at Columbus Junior High School will be in ear. Is it reasonable to make this prediction? Eplain. Enrollment Year m ; Possible ation of line of best fit: 00 Enrollment at Columbus Junior High School ; Possible enrollment prediction for : 99 students, which would be reasonable if the communities surroundthe school Students 500 continued tce 5 Year Copright b Holt, Rinehart and Winston. 56 Holt Mathematics