GeometryLesson 3 – 4

Equations of Lines

Objective:Write an equation of a line given information about the graph.

Solve problems by writing equations.

Equation Forms Slope-Intercept Formy = mx + bm – slopeb – y-intercept

Point-Slope Formy – y1 = m(x – x1)m – slope(x1, y1)

Write an equation in slope-intercept form of the line with slope 3 and y-

intercept of –2. Then graph the line.

y = mx + b

y = 3x – 2

Graphing:Put a dot on the y-intercept

(0, 3)Use slope (rise/run) to find more points.

Up 3 over 1

y = ½ x + 8

GraphingGraph (0, 8)Up 1 over 2

Write an equation in slope-intercept form of the line with slope ½ and y-intercept of

8. Then graph the line.

Don’t have to go by 2’s

Write an equation in point-slope form of the line with slope –3/4 that

contains (-2,5). Then graph.

y – y1 = m(x – x1)

24

35 xy (x – (-2))

Graphing: plot point, then use slope

Write an equation in point-slope of the line with slope of 4 that contains

(-3, -6). Then graph.

y + 6 = 4(x + 3)

Write an equation of the line through each points in slope-intercept form

(0, 3) and (-2, -1)

Method 1:

Find the slope m = 2

Use slope-intercept form Pick one of the points 3 = 2(0) + b b = 3

y = 2x + 3

Method 2: Find the slope m = 2

Use point-slope form Pick one of the points y – 3 = 2(x – 0)

Solve for y to put in slope-intercept form. y – 3 = 2(x – 0) y – 3 = 2x

y = 2x + 3

You may use either method

Write an equation of the line through each points in slope-intercept form

(-2, 4) & (8, 10)

5

3

10

6

82

104

m

b

2

5

34

b

5

64

b 45

6

5

26bb

5

20

5

6

5

26

5

3 xy

Write an equation of the line through (-2, 6) & (5, 6) in slope-intercept

form.

Find the slopem = 0 (horizontal line)

6 = 0(-2) + b

6 = b

y = 0x + 6

y = 6

Make sure you simplify.Do not leave 0x or 0

Horizontal & Vertical Lines

When an equation only has 1 variable it is either a horizontal or vertical line

The equation tells you how to graph.y = 6The line goes through the axis of the

variable given.A horizontal line at 6 through the y-axis.

Tell whether the following is a horizontal or vertical line.

y = 3

x = 6

x = -1

5 = y

-9 = x

x = 0

y = 0

horizontal

vertical

vertical

horizontal

vertical

Vertical (y-axis)

HorizontalX-axis

Write an equation in slope-intercept form for a line perpendicular to the line y = -3x

+ 2 through (4, 0).

Step 1: Identify slope for new equationm = 1/3 (because of perpendicular)

Write new equation with new slope and point.

b )4(3

10

b3

40

b3

43

4

3

1 xy

Write an equation is slope-intercept form for a line parallel to y = (-3/4)x

+ 3 containing (-3, 6)

Step 1: Identify slope for new equation (-3/4) same slope since parallel

Write new equation with new slope and point.

b )3(4

36

b4

96

b4

96

b4

15 4

15

4

3 xy

Homework

Pg. 200 1 – 12 all, 14 – 40 E