Section 3.5 Writing Equations of Lines 261 Enter the equation in the equation editor. 3 4 2 T u n + 6 ENTER Graph the equation and use the TRACE feature to determine if the points (-4, 0) and (4, 12) lie on the line. Press TRACE, enter the x-value of the first point and press enter. Notice that this takes us to the point (-4, 0) on the graph. RA H TRA E ( ) 4 ENTER Now enter the x-value of the second point. Notice that the display is x = 4 and y = 12. The point is not shown on the graph since it is outside of the standard viewing window. 4 ENTER Another way to check to see if the equation contains the points as solutions is to use the TABLE feature. Press 2nd RA H and verify that the points (4, 12) and (-4, 0) are in the table. SECTION 3.5 EXERCISE SET Write About It! Use complete sentences in your answer to each question. 1. How can you determine the equation of a line if you know its slope and y-intercept? 2. How can you determine the equation of a line if you know two points on the line? 3. Which method do you prefer to find the equation of a line—using the slope-intercept form or using the pointslope form? Why? 4. Explain how to determine the equation of the line that passes through the point (-1, 3) and is parallel to y = 4. 5. Explain how to determine the equation of the line that passes through the point (3, -2) and is perpendicular to 2x - 1 = 0. Determine if each statement is true or false. If a statement is false, explain why it is false. 6. The equation of the line with slope 7 that passes through the point (5, 0) is y = 7x + 5. 7. The equation of the line that passes through the point (2, 6) and is perpendicular to y = 3x + 4 is y=- 1 3 x + 6. 8. The equation of the line that passes through the point (3, -4) and is parallel to y = 3 - 2x is y = 3x - 13. Practice Makes Perfect! Write the equation of the line that satisfi es the given information. (See Objective 1.) 9. m = 4, b = 5 10. m = -2, b = 1 11. m = 3, passes through (0, -4) 12. m = 1 2 , passes through (0, 7) 13. m = - 2 3 with y-intercept (0, -10) 14. m = 4 5 with y-intercept (0, 20) 15. m = 0, passes through (0, 7) 16. m = 0, passes through (0, -14) 17. m = - 1 9 , passes through a0, - 4 9 b 18. m = 3 7 , passes through a0, 2 7 b Write the equation of the line that has the given slope and passes through the given point. Express each answer in slope-intercept form when possible. (See Objective 2.) 19. m = 4; (1, 5) 20. m = 2; (4, 3) 21. m = -5; (-2, -1) 22. m = 6; (3, 0) 23. m = -1; (-4, 0) 24. m = 1 2 ; (4, 0) 25. m = - 5 2 ; (-2, 0) 26. m = -7; (1, 6)
hendricks_beginning_intermediate_algebra_1e_ch1_3
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