1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) Objectives: The learner will.., Given two points, solve for slope, point-slope, and write an equation in slope-intercept form. Use the slope-intercept form to graph a line. 5.4 The Slope-Intercept Form NCSCOS 1.01, 1.02, 1.03, 3.03, 4.01

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y 2 – y 1 x 2 – x 1 m = Finding slope-intercept form from two points: 1) Solve for slope 2) Use point-slope form 5.4 The Slope-Intercept Form 3) From point-slope convert to slope-intercept form y = mx + b y – y 2 = m(x – x 2 ) y – y 1 = m(x – x 1 ) (x 1, y 1 ) (x 2, y 2 )

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 6 = 2(x – (-4)) y – 6 = 2(x + 4) y – 6 = 2x + 8 y = 2x + 14 m = 2 (-4, 6) 5.4 The Slope-Intercept Form y – 8 = 2(x – (-3)) y – 8 = 2(x + 3) y – 8 = 2x + 6 y = 2x + 14 m = 2 (-3, 8) y – y 1 = m(x – x 1 ) From the following two points, solve for slope, both point-slopes, and slope-intercept form: (-4, 6) (-3, 8) = 2 8 – 6 -3 – (-4) = 2 1 m = y – y 2 = m(x – x 2 )

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 5.4 The Slope-Intercept Form From the following two points, solve for slope, both point-slopes, and slope-intercept form: (–1, 3) (2, –3) y – y 1 = m(x – x 1 ) y – 3 = –2(x –(–1)) (-1, 3) m = – 2 (2, -3) m = – 2 y – 3 = –2(x + 1) y – 3 = –2x – 2 y = – 2x + 1 y – (-3) = –2(x – 2) y + 3 = –2(x – 2) y + 3 = –2x + 4 y = – 2x + 1 = – 2 -3 – 3 2 – (-1) = -6 3 m = y – y 2 = m(x – x 2 )

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 6 = (x + 8) y – 6 = x + 12 y = x + 18 m = (-8, 6) 5.4 The Slope-Intercept Form 3232 3232 3232 3232 y – 9 = (x + 6) y – 9 = x + 9 y = x + 18 m = (-6, 9) 3232 3232 3232 3232 From the following two points, solve for slope, both point-slopes, and slope-intercept form: (-8, 6) (-6, 9) 9 – 6 -6 – (-8) = 3 2 m =

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 5 = (x + 9) y – 5 = x + 12 y = x + 17 m =(-9, 5) 5.4 The Slope-Intercept Form 4343 4343 4343 4343 y – 9 = (x + 6) y – 9 = x + 8 y = x + 17 m = (-6, 9) 4343 4343 4343 4343 From the following two points, solve for slope, both point-slopes, and slope-intercept form : (-9, 5) (-6, 9) 9 – 5 -6 – (-9) = 4 3 m =

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 7 = – (x + 4) y – 7 = – x – 2 y = – x + 5 m = – (-4, 7) 5.4 The Slope-Intercept Form 1212 1212 1212 y – 0 = – (x – 10) y = – x + 5 (10, 0) 1212 1212 1212 m = – 1212 From the following two points, solve for slope, both point-slopes, and slope-intercept form: (-4, 7) (10, 0) 0 – 7 10 – (-4) = – 7 14 m = = – 1212

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 6 = – (x – 0) y – 6 = – x y = – x + 6 m = – (0, 6) 5.4 The Slope-Intercept Form 6565 6565 6565 y – 0 = – (x – 5) y = – x + 6 (5, 0) 6565 6565 6565 m = – 6565 From the following two points, solve for slope, both point-slopes, and slope-intercept form: (0, 6) (5, 0) y = – (x – 5) 6565 0 – 6 5 – 0 = – 6 5 m =

9. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 2 = (x – 7) (7, 2) 5.4 The Slope-Intercept Form (-4, -2) From the following two points, solve for slope, both point-slopes, and slope-intercept form: (7, 2) (-4, -2) m = 11 4 m = 4 11 4 y – 2 = x – 4 11 28 11 y = x – 4 11 6 y + 2 = (x + 4) 4 11 y + 2 = x + 4 11 16 11 y = x – 4 11 6 -2 – 2 -4 – 7 = 4 11 m =

10. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y + 3 = – (x + 4) y + 3 = – x – 6 y = – x – 9 m = – (-4, -3) 5.4 The Slope-Intercept Form 3232 3232 3232 3232 (-2, -6) m = – 3232 From the following two points, solve for slope, both point-slopes, and slope-intercept form: (-4, -3) (-2, -6) y + 6 = – (x + 2) y + 6 = – x – 3 y = – x – 9 3232 3232 3232 -6 – (-3) -2 – (-4) = – 3 2 m =

11. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 1 = – (x + 1) y – 1 = – x – y = – x – m = – (-1, 1) 5.4 The Slope-Intercept Form 4343 4343 4343 4343 (5, -7) m = – 4343 From the following two points, solve for slope, both point-slopes, and slope-intercept form : (-1, 1) (5, -7) 4343 1313 y + 7 = – (x – 5) y + 7 = – x + y = – x – 4343 4343 4343 20 1313 3 -7 – 1 5 – (-1) = – 8 6 m = = – 4 3

12. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) y – 8 = (x – 6) y – 8 = x – y = x + m =(6, 8) 5.4 The Slope-Intercept Form 4949 4949 4949 4949 y – 4 = (x + 3) y – 4 = x + m = (-3, 4) 4949 4949 4949 From the following two points, solve for slope, both point-slopes, and slope-intercept form : (6, 8) (-3, 4) 24 16 3 12 9 9 y = x + 4949 16 3 4 – 8 -3 – 6 = 4 9 m =

13. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 5.4 The Slope-Intercept Form From the following two points, solve for slope, both point-slopes, and slope-intercept form: (2, -5) (10, -5) = 0 y + 5 = 0(x – 2) y + 5 = 0 y = –5 m = 0 (2, -5) y + 5 = 0(x – 10) y + 5 = 0 y = –5 m = 0 (10, -5) -5 – (-5) 10 – 2 = m = 0 8

14. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) = undefined 5.4 The Slope-Intercept Form From the following two points, solve for slope, both point-slopes, and slope-intercept form: (3, 4) (3, -3) x = 3 -3 – 4 3 – 3 = – m = 7 0 x = 5 From the following two points, solve for slope, both point-slopes, and slope-intercept form: (5, -3) (5, 1) = undefined 1 – (-3) 5 – 5 = m = 4 0 no point-slope no slope-intercept no point-slope no slope-intercept

15. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 1) contains the origin and has a slope of –3 2) crosses the y-axis at -4, with a slope of 2 5.4 The Slope-Intercept Form Write an equation in slope-intercept form that fits each of the following descriptions: 3) crosses the y-axis at 3, with a slope of – 3434 4) crosses the y-axis at 1, with a slope of 2323 y = –3x + 0 y = 2x – 4 y = – x + 3 3434 y = x + 1 2323

16. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 1 8 7 6 5 4 3 2 y x 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2-1 -2 -3 -4 -5 -6 -7 -8 Graph the lines: y = 4x + 5 y = −2x – 4 y = − 4

17. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 1 8 7 6 5 4 3 2 y x 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2-1 -2 -3 -4 -5 -6 -7 -8 Graph the lines: y = 2x – 3 y = x + 4 1212 x = 5

18. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 1 8 7 6 5 4 3 2 y x 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2-1 -2 -3 -4 -5 -6 -7 -8 Graph the lines: y = −3x + 2 y = x – 8 2323 y = x – 3 4545

19. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. (Additional slides created/edited by Mr. Weidinger EWHS Goldsboro, NC) 1 8 7 6 5 4 3 2 y x 1 2 3 4 5 6 7 8 9 -9 -8 -7 -6 -5 -4 -3 -2-1 -2 -3 -4 -5 -6 -7 -8 Graph the lines: y = − x – 4 4343 y = x 2727 + 0 y = −0.5x + 4 y = − x + 4 1212