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

2. 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
b = –6
2. m = –1, x = 5, and y = –4
b = 1
y = 6x + 9
4. 4x – 2y = 8
y = 2x – 4

3. Objectives
Graph lines and write their equations in slope-intercept and point-slope form.
Classify lines as parallel, intersecting, or coinciding.

4. Vocabulary
point-slope form
slope-intercept form

6. A line with y-intercept b contains the point (0, b).
A line with x-intercept a contains the point (a, 0).
Remember!

7. 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

8. 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

9. 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

10. 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

11. Example 2A: Graphing Lines
Graph each line.
(0, 1)
rise 1
run 2

12. Example 2B: Graphing Lines
Graph each line.
y – 3 = –2(x + 4)
(–4, 3)
rise –2
run 1

13. Example 2C: Graphing Lines
Graph each line.
y = –3
(0, –3)

14. Check It Out! Example 2a Graph each line. y = 2x – 3 run 1 rise 2
(0, –3)
rise 2
run 1

15. 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

16. 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)

17. A system of two linear equations in two variables represents two lines
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. Example 3A: Classifying Pairs of Lines
Determine whether the lines are parallel, intersect, or coincide.
y = 3x + 7, y = –3x – 4

20. Example 3B: Classifying Pairs of Lines
Determine whether the lines are parallel, intersect, or coincide.

21. Example 3C: Classifying Pairs of Lines
Determine whether the lines are parallel, intersect, or coincide.
2y – 4x = 16, y – 10 = 2(x - 1)

22. 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. the line through (5, –1) with slope in point-slope form. 2 5
y + 1 = (x – 5)

23. Lesson Quiz: Part II
Determine whether the lines are parallel, intersect, or coincide. 1 2
3. y – 3 = – x,
y – 5 = 2(x + 3)
intersect
4. 2y = 4x + 12, 4x – 2y = 8
parallel