3-2 Solving Linear Equations by Graphing

Before we begin A short review http://www.youtube.com/watch?v=YPWlAY3y3_g https://www.youtube.com/watch?v=mxBoni8N70Y

Free graphing calculators for phonesI-phonehttps://itunes.apple.com/us/app/free-graphing-calculator/id378009553?mt=8Androidhttps://play.google.com/store/apps/details?id=com.algeo.algeo&hl=en

http://www.regentsprep.org/regents/math/algebra/ac1/eqlines2.htm

Essential Question:

Why are graphs useful?

Activities for today:Warm-upReview HWNew Lesson: Solving Linear Equations by GraphingIf 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

A short reviewDetermine 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 + 15.25 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?

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 RootSolve algebraically : 0 = ½ x + 3

Some more examplesSolve by graphing2 = x + 3

Solve algebraically-2 = x + 4

Some more examples Solve by graphing 6 = - x + 9

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

Some examples Solve 5x -7 = 5x + 2 graphically

Solve -3x + 6 = 7 – 3x algebraically

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.

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.

x x (x,y)

Real World ExamplesOn 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.

x x (x,y)