Chap3 Section4

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 3.4 The Point-Slope Form of a Line 305 Version: Fall 2007 3.4 Exercises In Exercises 1 - 4 , perform each of the following tasks. i. Draw the line on a sheet of graph paper with the given slope m that passes through the given point ( x 0 , y 0 ) . ii. Estimate the y -intercept of the line. iii. Use the point-slope form to determine the equation of the line. Place your answer in slope-intercept form by solv- ing for y . Compare the exact value of the y -intercept with the approxima- tion found in part (ii). 1. m = 2 / 3 and ( x 0 , y 0 ) = ( 1 , 1) 2. m = 2 / 3 and ( x 0 , y 0 ) = (1 , 1) 3. m = 3 / 4 and ( x 0 , y 0 ) = ( 2 , 3) 4. m = 2 / 5 and ( x 0 , y 0 ) = ( 3 , 2) 5. Find the equation of the line in slope- intercept form that passes through the point (1 , 3) and has a slope of 1 . 6. Find the equation of the line in slope- intercept form that passes through the point (0 , 2) and has a slope of 1 / 4 . 7. Find the equation of the line in slope- intercept form that passes through the point (1 , 9) and has a slope of 2 / 3 . 8. Find the equation of the line in slope- intercept form that passes through the point (1 , 9) and has a slope of 3 / 4 . Copyrighted material. See: 1 In Exercises 9 - 12 , perform each of the following tasks. i. Set up a coordinate system on a sheet of graph paper and draw the line through the two given points. ii. Use the point-slope form to determine the equation of the line. iii. Place the equation of the line in stan- dard form Ax + By = C , where A , B , and C are integers and A > 0 . Label the line in your plot with this result. 9. ( 2 , 1) and (3 , 2) 10. ( 1 , 4) and (2 , 3) 11. ( 2 , 3) and (4 , 3) 12. ( 4 , 4) and (2 , 4) 13. Find the equation of the line in slope- intercept form that passes through the points ( 5 , 5) and (6 , 8) . 14. Find the equation of the line in slope- intercept form that passes through the points (6 , 6) and (9 , 7) . 15. Find the equation of the line in slope- intercept form that passes through the points ( 4 , 6) and (2 , 4) . 16. Find the equation of the line in slope- intercept form that passes through the points ( 1 , 5) and (4 , 4) .

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306 Chapter 3 Linear Functions Version: Fall 2007 In Exercises 17 - 20 , perform each of the following tasks. i. Draw the graph of the given linear equation on graph paper and label it with its equation. ii. Determine the slope of the given equa- tion, then use this slope to draw a second line through the given point P that is parallel to the first line. iii. Estimate the y -intercept of the sec- ond line from your graph. iv. Use the point-slope form to determine the equation of the second line. Place this result in slope-intercept form y = mx + b , then state the exact value of the y -intercept. Label the second line with the slope-intercept form of its equation. 17. 2 x + 3 y = 6 , P = ( 2 , 3) 18. 3 x 4 y = 12 , P = ( 3 , 4) 19. x + 2 y = 4 , P = (3 , 3) 20. 5 x + 2 y = 10 , P = ( 3 , 5) In Exercises 21 - 24 , perform each of the following tasks.
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