1. Example 1 Write an Equation Given Slope and a Point
Example 2 Write an Equation of a Horizontal Line
Example 3 Write an Equation in Standard Form
Example 4 Write an Equation in Slope-Intercept Form
Example 5 Write an Equation in Point-Slope Form
Lesson 5 Contents

2. Answer: The equation is
Write the point-slope form of an equation for a line that passes through (–2, 0) with slope
Point-slope form
Simplify.
Answer: The equation is
Example 5-1a

3. Write the point-slope form of an equation for a line that passes through (4, –3) with slope –2.
Answer:
Example 5-1b

4. Answer: The equation is
Write the point-slope form of an equation for a horizontal line that passes through (0, 5).
Point-slope form
Simplify.
Answer: The equation is
Example 5-2a

5. Write the point-slope form of an equation for a horizontal line that passes through (–3, –4).
Answer:
Example 5-2b

6. Write in slope-intercept form.
In slope-intercept form, y is on the left side of the equation. The constant and x are on the right side.
Original equation
Distributive Property
Add 5 to each side.
Example 5-4a

7. Answer: The slope-intercept form of the equation is
Simplify.
Answer: The slope-intercept form of the equation is
Example 5-4b

8. Write in slope-intercept form.
Answer:
Example 5-4c

9. The figure shows trapezoid ABCD with bases and
Write the point-slope form of the lines which are NOT the bases of the trapezoid.
Example 5-5a

10. The figure shows right triangle ABC.
a. Write the point-slope form of the line containing the hypotenuse
Answer:
Example 5-5f

11. Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48
1) 10
2) 48
3) 7
Find the greatest common factor (GCF) of each set of numbers.
4) 6,14
5) 12,18,30
6) 4,8,15,20

12. Factoring Quadratic Expressions
Objectives:
Factor a quadratic expression

13. Example 1 Factor each quadratic expression. a) 27x2 – 18x 27 x2 18 x
factor out the GCF for all terms 9 x
(3x – 2)
b) 5x(2x + 1) – 2(2x + 1)
(2x + 1)
(2x + 1)
factor out the GCF for all terms
(2x + 1)
( )
5x - 2

14. Factoring x2 + bx + c
To factor an expression of the form ax2 + bx + c, where a = 1, look for integers r and s such that r s = c and r + s = b. Then factor the expression.
x2 + bx + c =
(x + r)(x + s)

15. Example 2
Factor x2 + 12x + 27.
( ) x + 3
( ) x + 9

16. Example 3
Factor x2 - 15x - 54.
( ) x + 3
( ) x - 18

17. Example 4
Factor 5x2 + 14x + 8.
( ) 5x + 4
( ) x + 2

18. Practice Factor. 1) 5x2 + 15x 2) (2x – 1)4 + (2x – 1)x 3) x2 + 9x + 20

19. Homework
p.296 #31,35,37,39,41,43,45,49,53,57

20. Practice 6 minutes Factor. 1) 3x2 - 15x 2) (3x + 7)x + (3x + 7)8

21. Special Products Factoring the Difference of Two Squares
a2 – b2 = (a + b)(a – b)
Factoring Perfect-Square Trinomials
a2 + 2ab + b2 = (a + b)(a + b)
a2 - 2ab + b2 = (a - b)(a - b)

22. Example 1
Factor x
( ) x + 4
( ) x - 4

23. Example 2 Factor x4 - 81. ( ) x2 + 9 ( ) x2 - 9 (x2 + 9) ( ) x + 3 ( )
( ) x2 + 9
( ) x2 - 9
(x2 + 9)
( ) x + 3
( ) x - 3

24. Example 3 Factor 2x2 – 24x + 72. 2 24 72 2 ( ) x2 – 12x + 36 2( )( )
( )
x2 – 12x + 36
2( )( )
x - 6
x - 6