Example 1 Write an Equation Given Slope and a Point

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

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

Factoring Quadratic Expressions Objectives: Factor a quadratic expression

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

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)

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

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

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

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

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

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

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)

Example 1 Factor x2 - 16. ( ) x + 4 ( ) x - 4

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

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