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LESSON 3–2

LESSON 3–2. Zeroes of Linear Functions. Determine whether y = – 2 x – 9 is a linear equation. If it is, write the equation in standard form. 5-Minute Check 1. Determine whether 3 x – xy + 7 = 0 is a linear equation. If it is, write the equation in standard form. 5-Minute Check 2.

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LESSON 3–2

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  1. LESSON 3–2 Zeroes of Linear Functions

  2. Determine whether y = –2x – 9 is a linear equation. If it is, write the equation in standard form. 5-Minute Check 1

  3. Determine whether 3x – xy + 7 = 0 is a linear equation. If it is, write the equation in standard form. 5-Minute Check 2

  4. Graph y = –3x + 3. 5-Minute Check 3

  5. Jake’s Windows uses the equation c = 5w + 15.25 to calculate the total charge c based on the number of windows w that are washed. What will be the charge for washing 15 windows? 5-Minute Check 4

  6. Which linear equation is represented by this graph? A. x - y = 3 B. -2x + y = 1 C. x - y = -3 D. -2x + y = -3 5-Minute Check 5

  7. Targeted TEKS A.2(B) Write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x - x1), given one point and the slope and given two points. A.3(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems. Also addresses A.2(A). Mathematical Processes A.1(B), A.1(C) TEKS

  8. You graphed linear equations by using tables and finding roots, zeros, and intercepts. • Find zeros of linear functions. • Model linear functions. Then/Now

  9. linear function • parent function • family of graphs • root • zeros Vocabulary

  10. Concept

  11. Find Zeros of a Linear Function Graphically Example 1 A

  12. Solve an Equation with One Root Example 1 B

  13. Example 1 CYP B

  14. Find Zeros of a Linear FunctionAlgebraically TRAVELING Maria’s car can travel 420 miles on a 12-gallon tank of gas. The equation y = 420 – 12x describes the distance she can travel on a full tank of gas if her fuel mileage is x miles per gallon. Find the zero and describe what it means in the context of the situation. Identify the domain and range and describe their significance. Example 2

  15. Estimate by Graphing FUNDRAISING Kendra’s class is selling greeting cards to raise money for new soccer equipment. They paid $115 for the cards, and they are selling each card for $1.75. The function y = 1.75x – 115 represents their profit y for selling x greeting cards. Find the zero of this function. Describe what this value means in this context. Example 3

  16. TRAVEL On a trip to his friend’s house, Raphael’s average speed was 45 miles per hour. The distance that Raphael is from his friend’s house at a certain moment in the trip can be represented by d = 150 – 45t, where d represents the distance in miles and t is the time in hours. Find the zero of this function. Describe what this value means in this context. • A • B • C • D Example 3

  17. LESSON 3–2 Zeroes of Linear Functions

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