Graphing Linear Functions Using Slope Intercept Form

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Objective

SWBAT write a linear model in slope intercept form. SWBAT understand the meaning and application of slope and y-intercept.

Big Idea

Slope and y-intercept have specific meaning based on the context of a problem. They can also help in making predictions about a function.

Launch

15 minutes

At the beginning of class, display slope_intercept_form_launch and let the students try to understand what the table is saying (MP1).  Have students write down at least two things that they notice about the cost of going to the fair.  You are not looking for anything specific at this point.  This is just giving students time to read and process. 

Next, allow students to work with their partners to answer the four questions on Slide 2. Students will approach these questions in many different ways.  Try not to guide students in to one particular way of thinking.  If students are stuck, question them to find out what they know and then guide them in the right direction based on their current train of thought.  

While students are working and discussing listen to the approaches that students are taking.  Make note of which pairs are trying which approach.  Some approaches may be more sophisticated than others (multiplicative reasoning vs. additive reasoning) (MP2).  

Take a few minutes once students have finished to discuss the answers.  Try to call on as many students as possible to share their ideas starting with less sophisticated and moving towards more sophisticated.  Let students do most of the talking by guiding the conversation and asking good questions but not giving answers.  Have students build on each other's ideas rather than simply stating their own ideas (MP3).  This will help students develop the skill of listening to each other. 

Direct Instruction

5 minutes

 

Students should be familiar with the slope-intercept form of an equation from middle school.  You have also worked to develop this concept over the preceeding lessons.  Show students how the rate of change (slope) and y-intercept (x-value of zero) fit in with their 4th answer from the launch.  Refer back to the context of the launch to ensure that students are making the connection with this equation (for example, the cost of each ticket is 50 cents which is represented by 0.5x and the cost to enter the fair is $5 represented by the + 5)  Students can then graph the function by starting at the y-intercept and plotting further coordinates by using a slope of 0.5.  In this section you can also discuss the domain and range of this function.  Explain to students that while this function is actually discrete, the model of the situation can be drawn as a continuous function.

The third slide is a predictive question.  Have students do a think-pair-share around this question.  Have students verify their answer by substituting their answer back into the function to determine if their answer makes sense (MP6).

Practice

15 minutes

Have students work in pairs on the two tasks in slope_intercept_form_practice.  Students should concentrate on determining the meaning of the slope and y-intercept in the context of the problem (MP4).  Students will also be answering a predictive question on each of the practice problems that will require them to find the independent variable given a specific dependent variable value (MP2). 

Closure

5 minutes

This question is very open ended and could lead to some fairly interesting answers.  The idea here is that both of these functions mentioned have a domain that essentially goes to infinity.  In the real world, charges don't always increase forever.  The bank will eventually forclose on the house, the repo man will take the car back, you "buy" the movie from Netflix, etc.  Sometimes we need to ground our mathematical work in the real world.  Students need to understand that mathematical models are just that...models.  The models have great utility, but sometimes only on a given domain.

This idea comes into play in both scenarios studied today.  Hopefully students will recognize that the fair will close at some point and so you can't continue buying tickets to go on the rides.  With the same idea in mind, you will have to bring the canoe back eventually, or you will take it or sink it.  In either case you will have to pay for the canoe and probably be in some legal trouble as well!