1. Point-Slope Form 4.5 1.Use point-slope form to write the equation of a line. 2.Write the equation of a line parallel to a given line. 3.Write the equation of a line perpendicular to a given line.

2. Practice …… 1. Write in standard form:2. Write in standard form: 3. Write in standard form:4. Write in standard form:

3. Practice …… 1. Write in standard form:2. Write in standard form: 3. Write in slope-intercept form:4. Write in slope-intercept form:

4. Objective 1 Use point-slope form to write the equation of a line.

5. Point Slope Form Given two points (x 1, y 1 ) and (x, y) Use whenever you want to write an equation! Need to know a point and a slope.

6. Write the equation of a line with a slope of 5 and passing through the point (3, 12) in slope-intercept form. y – y 1 = m(x – x 1 ) m = 5, x 1 = 3, y 1 = 12 Write the equation in standard form. Slope: y – y 1 = m(x – x 1 ) y – 12 = 5(x – 3) y – 12 = 5x – 15 Distribute. y = 5x – 3 Add 12 to both sides to isolate y. (3, 12) Point: 5 y – 12 = 5x – 15 -5x + y -12 = -15 -5x + y = -3 5x – y = 3

7. Write the equation of a line passing through (-1, -5) and (-4, 1) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point: Slope: (-1, -5) slope-interceptstandard form

8. Write the equation of a line with a slope of and passing through the point (-3, 5) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point:Slope: (-3, 5) slope-interceptstandard form

9. Write the equation of a line passing through (2, -4) and (3, -4) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point:Slope: (2, -4) Horizontal line Intersects only the y-axis. Equation has only a y. y = -4

10. Write the equation of a line passing through (-2, 5) and (-2, -6) in slope-intercept and standard form. y – y 1 = m(x – x 1 ) Point: Slope: (-2, 5) Vertical line Intersects only the x-axis. Equation has only an x. x = -2

11. Objective 2 & 3 Write the equation of a line parallel to a given line. Write the equation of a line perpendicular to a given line.

12. Parallel Lines The slopes of parallel lines are equal. y = 2x + 1 y = 2x – 3

13. Perpendicular Lines The slopes of perpendicular lines are negative reciprocals.

14. The only way to determine if lines are parallel or perpendicular is to compare the slopes.

15. Parallel or Perpendicular? Parallel m = 3 Neither m = 5 m = -5 Perpendicular horizontal vertical Perpendicular

16. y – y 1 = m(x – x 1 ) y – (  5) = –3(x – 1) y + 5 = –3x + 3 y = –3x – 2 (1, -5) Write the equation of a line that passes through (1, –5) and parallel to y = –3x + 4. Write the equation in slope-intercept form. y – y 1 = m(x – x 1 )Need a point and slope m = -3

17. Write the equation of a line that passes through (3, 7) and perpendicular to 5x + 2y = 3. Write the equation in standard form. (3, 7) y – y 1 = m(x – x 1 )Need a point and slope

18. Slide 4- 18 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write the equation of the line in slope-intercept form given m =  2 and the point (4,  5). a) y =  2x – 3 b) y = 2x + 3 c) y =  2x + 3 d) y =  2x – 5

19. Slide 4- 19 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Write the equation of the line in slope- intercept form given m =  2 and the point (4,  5). a) y =  2x – 3 b) y = 2x + 3 c) y =  2x + 3 d) y =  2x – 5

20. Slide 4- 20 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the equation of the line connecting the points (4,  3) and (  1, 7) in slope- intercept form? d) a) y =  2x + 5 b) y = 2x + 5 c) y =  2x – 5

21. Slide 4- 21 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the equation of the line connecting the points (4,  3) and (  1, 7)? a) y =  2x + 5 b) y = 2x + 5 c) y =  2x – 5 d)

22. Slide 4- 22 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the relationship between the two lines? 5x – 3y = 11 3x + 5y = 8 a) parallel b) perpendicular c) neither

23. Slide 4- 23 Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley What is the relationship between the two lines? 5x – 3y = 11 3x + 5y = 8 a) parallel b) perpendicular c) neither