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4-1 Writing Linear Equations in Slope-Intercept Form

4-1 Writing Linear Equations in Slope-Intercept Form. Goals: Use the slope and y-intercept to write the equation of a line. Model a real-life situation with a linear equation. Vocabulary. Slope-Intercept Form – an equation in the form y = mx + b. Slope is m y-intercept is b. Example.

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4-1 Writing Linear Equations in Slope-Intercept Form

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  1. 4-1 Writing Linear Equations in Slope-Intercept Form Goals: Use the slope and y-intercept to write the equation of a line. Model a real-life situation with a linear equation.

  2. Vocabulary • Slope-Intercept Form – an equation in the form y = mx + b. • Slope is m • y-intercept is b.

  3. Example Write the equation of the line whose slope is -2 and whose y-intercept is 5. y = mx + b y = x + y = -2x + 5 m b -2 5

  4. Examples Write an equation in slope-intercept form. • Slope is 3, y-intercept is -5 y = 3x – 5 • m = -3, b = 6 y = -3x + 6 • Slope is – ½, y-intercept is -4 y = - ½ x – 4

  5. Write an equation in slope-intercept form of the line whose slope is 4 and whose y-intercept is 3. A.y = 3x + 4 B.y = 4x + 3 C.y = 4x D.y = 4

  6. Write the equation of each graph. 1. 2.

  7. A. B. C. D. Example #3 Which of the following is an equation in slope-intercept form for the line shown in the graph?

  8. A. B. C. D. Which of the following is an equation in slope-intercept form for the line shown in the graph?

  9. Practice Write an equation in slope-intercept form. • m = 5, b = 8 • Slope is 6, y-intercept is – 3 • b = 4, m = ¼ • y-intercept is 2, slope is -6 • m = 1, b = 0 • y = 5x + 8 • y = 6x – 3 • y = ¼ x + 4 • y = -6x + 2 • y = x

  10. Word Problems • Slope is rate of change!!! • Look for words like per, for each, for every… • y-intercept is the beginning amount • Look for words like beginning, initial…

  11. Word Problem #1 Your family decides to rent bikes while you are on vacation. It costs $4 to rent the bike, plus $1.50 per hour. • Write an equation in slope-intercept form that models this situation. y = 1.5x + 4 • How much will it cost to rent the bike for 12 hours? $22

  12. Word Problem #2 In 1990, the population in California was 29.76 million. During the next 25 years, the population increased by .31 million people per year. • Write an equation in slope-intercept form that models this situation. y = .31x + 29.76 • How many people were there in California in 2005? 34.41 million people

  13. Word Problem #3 A telephone call costs $3.44 for the first minute, and $.24 for each additional minute. • Write an equation in slope-intercept form that models this situation. y = .24x + 3.44 • How much will it cost for a 9 minute phone call? $5.36

  14. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Write a linear equation to find the average amount D spent for any year n since 1986. A.D = 0.15n B.D = 0.15n + 3 C.D = 3n D.D = 3n + 0.15

  15. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Find the amount spent by consumers in 1999. A. $5 million B. $3 million C. $4.95 million D. $3.5 million

  16. Homework • Pages 220-221 #11-22 #37, 50,51 You do not have to graph any equations!

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