1. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane 3-6 Lines in the Coordinate Plane Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry

2. 3-6 Lines in the Coordinate Plane Warm Up Substitute the given values of m, x, and y into the equation y = mx + b and solve for b. 1. m = 2, x = 3, and y = 0 Solve each equation for y. 3. y – 6x = 9 2. m = –1, x = 5, and y = –4 b = –6 b = 1 4. 4x – 2y = 8 y = 6x + 9 y = 2x – 4

3. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding. Objectives

4. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane point-slope form slope-intercept form Vocabulary

5. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane The equation of a line can be written in many different forms. The point-slope and slope-intercept forms of a line are equivalent. Because the slope of a vertical line is undefined, these forms cannot be used to write the equation of a vertical line.

6. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane

7. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Graph each line. Example 2A: Graphing Lines The equation is given in the slope-intercept form, with a slope of and a y-intercept of 1. Plot the point (0, 1) and then rise 1 and run 2 to find another point. Draw the line containing the points. (0, 1) rise 1 run 2

8. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Graph each line. Example 2B: Graphing Lines y – 3 = –2(x + 4) The equation is given in the point-slope form, with a slope of through the point (–4, 3). Plot the point (–4, 3) and then rise –2 and run 1 to find another point. Draw the line containing the points. (–4, 3) rise –2 run 1

9. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Graph each line. Example 2C: Graphing Lines The equation is given in the form of a horizontal line with a y-intercept of –3. The equation tells you that the y-coordinate of every point on the line is –3. Draw the horizontal line through (0, –3). y = –3 (0, –3)

10. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 2a Graph each line. y = 2x – 3 The equation is given in the slope-intercept form, with a slope of and a y-intercept of –3. Plot the point (0, –3) and then rise 2 and run 1 to find another point. Draw the line containing the points. (0, –3) rise 2 run 1

11. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 2b Graph each line. The equation is given in the point-slope form, with a slope of through the point (–2, 1). Plot the point (–2, 1)and then rise –2 and run 3 to find another point. Draw the line containing the points. (–2, 1) run 3 rise –2

12. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 2c Graph each line. y = –4 The equation is given in the form of a horizontal line with a y-intercept of –4. The equation tells you that the y-coordinate of every point on the line is –4. Draw the horizontal line through (0, –4). (0, –4)

13. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Example 1A: Writing Equations In Lines Write the equation of each line in the given form. the line with slope 6 through (3, –4) in point- slope form y – y 1 = m(x – x 1 ) y – (–4) = 6(x – 3) Point-slope form Substitute 6 for m, 3 for x 1, and -4 for y 1.

14. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Example 1B: Writing Equations In Lines Write the equation of each line in the given form. the line through (–1, 0) and (1, 2) in slope- intercept form y = x + 1 Find the slope. Write in slope-intercept form using m = 1 and b = 1.

15. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Example 1C: Writing Equations In Lines Write the equation of each line in the given form. the line with the x-intercept 3 and y-intercept –5 in point slope form

16. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 1a Write the equation of each line in the given form. the line with slope 0 through (4, 6) in slope- intercept form y = 6 y – y 1 = m(x – x 1 ) y – 6 = 0(x – 4) Point-slope form Substitute 0 for m, 4 for x 1, and 6 for y 1.

17. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 1b Write the equation of each line in the given form. the line through (–3, 2) and (1, 2) in point- slope form y - 2 = 0 Find the slope. y – y 1 = m(x – x 1 ) Point-slope form Simplify. Substitute 0 for m, 1 for x 1, and 2 for y 1. y – 2 = 0(x – 1)

18. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane A system of two linear equations in two variables represents two lines. The lines can be parallel, intersecting, or coinciding. Lines that coincide are the same line, but the equations may be written in different forms.

19. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane

20. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3A: Classifying Pairs of Lines y = 3x + 7, y = –3x – 4 The lines have different slopes, so they intersect.

21. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3B: Classifying Pairs of Lines Solve the second equation for y to find the slope- intercept form. 6y = –2x + 12 Both lines have a slope of, and the y-intercepts are different. So the lines are parallel.

22. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Determine whether the lines are parallel, intersect, or coincide. Example 3C: Classifying Pairs of Lines 2y – 4x = 16, y – 10 = 2(x - 1) Solve both equations for y to find the slope- intercept form. 2y – 4x = 16 Both lines have a slope of 2 and a y-intercept of 8, so they coincide. 2y = 4x + 16 y = 2x + 8 y – 10 = 2(x – 1) y – 10 = 2x - 2 y = 2x + 8

23. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Check It Out! Example 3 Determine whether the lines 3x + 5y = 2 and 3x + 6 = -5y are parallel, intersect, or coincide. Both lines have the same slopes but different y-intercepts, so the lines are parallel. Solve both equations for y to find the slope- intercept form. 3x + 5y = 2 5y = –3x + 2 3x + 6 = –5y

24. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Lesson Quiz: Part I Write the equation of each line in the given form. Then graph each line. 1. the line through (-1, 3) and (3, -5) in slope- intercept form. y = –2x + 1 2 5 y + 1 = (x – 5) 2. the line through (5, –1) with slope in point-slope form.

25. Holt McDougal Geometry 3-6 Lines in the Coordinate Plane Lesson Quiz: Part II Determine whether the lines are parallel, intersect, or coincide. 3. y – 3 = – x, intersect 1 2 y – 5 = 2(x + 3) 4. 2y = 4x + 12, 4x – 2y = 8 parallel