Lesson Menu Five-Minute Check over Lesson 3 1

Lesson Menu Five-Minute Check (over Lesson 3– 1) Mathematical Practices Then/Now New Vocabulary Key Concept: Linear Equation Example 1: Find Zeros of a Linear Function Graphically Example 2: Real World Example: Find Zeros of a Linear Function Algebraically Example 3: Real-World Example: Estimate a Zero by Graphing

Over Lesson 3– 1 Determine whether y = – 2 x – 9 is a linear equation. If it is, write the equation in standard form. A. linear; y = 2 x – 9 B. linear; 2 x + y = – 9 C. linear; 2 x + y + 9 = 0 D. not linear

Over Lesson 3– 1 Determine whether 3 x – xy + 7 = 0 is a linear equation. If it is, write the equation in standard form. A. linear; y = – 3 x – 7 B. linear; y = – 3 x + 7 C. linear; 3 x – xy = – 7 D. not linear

Over Lesson 3– 1 Graph y = – 3 x + 3. A. B. C. D.

Over Lesson 3– 1 Jake’s Windows uses the equation c = 5 w + 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? A. $75. 00 B. $85. 25 C. $87. 50 D. $90. 25

Over Lesson 3– 1 Which linear equation is represented by this graph? A. y = x – 3 B. y = 2 x + 1 C. y = x + 3 D. y = 2 x – 3

Mathematical Practices 4 Model with mathematics. Content Standards A. REI. 10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F. IF. 7 a Graph linear and quadratic functions and show intercepts, maxima, and minima.

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

• linear function • parent function • family of graphs • Root zeros

Find Zeros of a Linear Function Graphically Find the zero of each linear function by graphing. A. Graph the equation. Where does the line cross the x-axis? (– 6, 0) The x value of the coordinate is the zero of the function. – 6 Answer: – 6.

Find Zeros of a Linear Function Graphically Find the zero of each linear function by graphing. B. Graph the equation. Where does the line cross the x-axis? (– 3, 0) The x value of the coordinate is the zero of the function. – 3 Answer: – 3.

Find Zeros of a Linear Function Algebraically TRAVELING Maria can go 420 miles on a 12 -gallon tank of gas. The equation y = 420 – 12 x 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 situatiaon. Identify the domain and range and describe their significance. Graph the equation. Where does the line cross the x- axis? (35, 0) The x value of the coordinate is 35 Maia’s miles per gallon. Where does the line cross the y- axis? (0, 420)

Find Zeros of a Linear Function Algebraically The y value of the coordinate is the zero of the number of miles Maria can travel. 420 What are the x values covered by the graph? This is the Domain of the graph. D = {x | 0 ≤ x ≤ 35} What are the y values covered by the graph? This is the Range of the graph. R = {y | 0 ≤ y ≤ 420} The Domain represents the miles per gallon and the range represents the miles traveled. Answer: 35; Maria can get 35 miles to the gallon; D = {x | 0 ≤ x ≤ 35}, R = {y | 0 ≤ y ≤ 420}

A. Solve – 3 x + 6 = 7 – 3 x algebraically. A. x = 0 B. x = 1 C. x = – 1 D. no solution

B. Solve 4 – 6 x = – 6 x + 3 by graphing. A. x = – 1 B. x = 1 C. x=1 D. no solution

Estimate a Zero 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. 75 x – 115 represents their profit y for selling x greeting cards. Find the zero and describe what it means in the context of this situation. Identify the domain and range. Graph the function. The graph appears to intersect the x-axis at 65.

Estimate a Zero by Graphing Use algebra to find the x-intercept, or zero, which is about 65. 71. Since Kendra’s class cannot sell part of a greeting card, they must sell 66 cards to make a profit. The domain is {x | x ≥ 0}, where r is an integer. The range is {y | y ≥ – 115}. Answer: The domain is {x | x ≥ 0}, where r is an integer. The range is {y | y ≥ – 115}.

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 – 45 t, 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. 3; Raphael will arrive at his friend’s house in 3 hours. B. Raphael will arrive at his friend’s house in 3 hours 20 minutes. C. Raphael will arrive at his friend’s house in 3 hours 30 minutes. D. 4; Raphael will arrive at his friend’s house in 4 hours. A. B. C. D. A B C D