Objectives:

1
Equations of Lines

• Objectives
• Be able to find the equation of a line (FTEOTL)
  when given the slope and a point on the graph.
• Be able to find the equation of a line (FTEOTL)
  when given two points on the graph.

Critical Vocabulary Point-Slope Form Slope
Intercept Form.

• Daily Warm UP
• Find the slope and y-intercept 3x - 6y 20
• Graph 2x y 3

2

• Daily Warm UP
• Find the slope and y-intercept 3x - 6y 20
• Graph 2x y 3

3
The Point Slope form of the equation of the line
through (x1, y1) with a slope m is given by the
formula
y y1 m (x - x1)
I. FTEOTL given the slope and a point
Example 1 Find the equation of the line in
point-slope form that goes through
the point (2, -6) and has a slope of 5
1. What is the slope?
m 5

• What is another point on
• the graph?

(2, -6)

• Substitute into the point
• slope equation.

Y - -6 5(x - 2)
Y 6 5(x - 2)
Y 6 5x - 10
- 6 - 6
Y 5x - 16
4
The Point Slope form of the equation of the line
through (x1, y1) with a slope m is given by the
formula
y y1 m (x - x1)
I. Write an equation from Point-slope form into
SIF
Example 2 Write the equation of the line that
goes through the point
(6,-2) and has a slope of ½ into SIF
Y 2 ½(x 6)
(Point-slope Form)
Y 2 ½x 3
- 2 - 2
Y ½x 5
5
The Point Slope form of the equation of the line
through (x1, y1) with a slope m is given by the
formula
y y1 m (x - x1)
II. FTEOTL given two points
Example 1 FTEOTL that goes through the points
(3, -1) and (4, 2)
1st Find the Slope
2nd Put into Point Slope Form
3rd Put into SIF
2 2
6
The Point Slope form of the equation of the line
through (x1, y1) with a slope m is given by the
formula
y y1 m (x - x1)
II. FTEOTL given two points
Example 2 FTEOTL that goes through the points
(-4, 5) and (2, 2)
1st Find the Slope
2nd Put into Point Slope Form
3rd Put into SIF
2 2
7
The Point Slope form of the equation of the line
through (x1, y1) with a slope m is given by the
formula
y y1 m (x - x1)
II. FTEOTL given two points
Example 3 FTEOTL that goes through the points
(5, 2) and (-2, 3)
1st Find the Slope
2nd Put into Point Slope Form
3rd Put into SIF
5 5
8
Read Pages 94-96 HW Page 97-98 28-33, 44-49
(12 problems)