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3-2 Solving Linear Equations by Graphing

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Before we begin A short review https://www.youtube.com/watch?v=mxBoni8N70Y Free graphing calculators for phones I-phone https://itunes.apple.com/us/app/free- graphing-calculator/id ?mt=8 Android https://play.google.com/store/apps/details?i d=com.algeo.algeo&hl=en algebra/ac1/eqlines2.htm Essential Question: Why are graphs useful? Activities for today: Warm-up Review HW New Lesson: Solving Linear Equations by Graphing If time: work on homework and/or project I will be able to…. Solve linear equations by graphing Estimate solutions to a linear equation by graphing

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A short review Determine whether y= -2x -9 is a linear equation. Determine whether 3x – xy + 7 = 0 is a linear equation. If it is, write the equation in standard form. Graph y = -3x + 3 Jake’s Windows used the equation c= 5w to calculation the total charge c based on the number of windows w that are washed. What will be the charge for washing 15 windows?

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A short review/ Let’s begin the lesson Which linear equation is represented by this graph? A.y = x – 3 B.y = 2x + 1 C.y = x + 3 D.y = 2x – 3 New vocabulary: Linear function Parent function Family of graphs Root Zeros Solve an Equation with One Root Solve algebraically : 0 = ½ x + 3

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Some more examples

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Solve 2x + 5 = 2x + 3 algebraically.

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Some examples Solve 5x -7 = 5x + 2 graphically Solve -3x + 6 = 7 – 3x algebraically

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Some more examples Solve 4- 6x = -6x + 3 by graphing Recap: An equation can be solved by graphing or algebraically. A linear equation can have one root, all real numbers or no answers.

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Real World Examples Kendra’s calss 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. thefunction y = 1.75x – 115 represents their profit y for selling x greeting cards. Find the zero of the this value means in this context. Make a table and graph. xx(x,y)

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Real World Examples 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 repesents the distance in miles and t is the time in hours. Find the zero of the this value means in this context. Make a table and graph. xx(x,y)

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