Chapter 3 3-6 Lines in the coordinate plane

ObjectivesGraph lines and write their equations in

slope-intercept and point-slope form.Classify lines as parallel, intersecting, or

coinciding.

Equation of a line 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.

Forms of the equation of a line

Example#1 Write the equation of each line in

the given form. the line with slope 6 through (3, –4)

in point-slope form.

Example#2 Write the equation of each line in

the given form. the line through (–1, 0) and (1, 2) in

slope-intercept form.

Example#3 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.

Student guided practice Do problems 2-4 in your book page 194

Graphing Equations of the line Graph each line.

(0, 1)

rise 1run 2

Example#4 Graph each line. y – 3 = –2(x + 4)

(–4, 3)rise –2

run 1

Example#5 Graph each line. y = –3

(0, –3)

Example#6 Graph each line. x= 4

Student guided practice Do problems 5-7

Equations of 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.

Pair of lines

Example#7 Determine whether the lines are

parallel, intersect, or coincide. y = 3x + 7, y = –3x – 4 The lines have different slopes, so they

intersect.

Example#8 Determine whether the lines are

parallel, intersect, or coincide.

Both lines have a slope of -1/3, and the y-intercepts are different. So the lines are parallel.

Example#9 Determine whether the lines are

parallel, intersect, or coincide. 2y – 4x = 16, y – 10 = 2(x - 1) Both lines have a slope of 2 and a y-

intercept of 8, so they coincide.

Student guided practice Do problems 8-11 in your book page

194

Problem solving application Erica is trying to decide between

two car rental plans. For how many miles will the plans cost the same?

Lesson Quiz Identify each of the following: 1. a pair of parallel segments 2. a pair of skew segments

Lesson Quiz State the theorem or postulate that is

related to the measures of the angles in each pair. Then find the unknown angle measures.

3. m3 = (50x + 20)°, m4= (100x – 80)° 4. m3 = (45x + 30)°, m5 = (25x + 10)°

Lesson Quiz Use the theorems and given

information to prove p || r. 5. m2 = (5x + 20)°, m 7 = (7x + 8)°,

and x = 6