# Unit 1: Linear Equations

### y-intercept

## Learning Target: I can identify the y-intercept

__Common Core Standards:__

**8.EE.5:** Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

**8.EE.6:** Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

**8.EE.7:** Solve linear equations in one variable.

**Students will know:**

- what the
*b*in*y=mx+b*represents - what the y-intercept is

**Students will be able to:**

- identify the y-intercept from the equation
*y=mx+b* - find the y-intercept or
*b*on a graph

**Essential Questions:**

1. What is the y-intercept?

2. What does the *b* represent in the equation *y=mx+b*

3. How do we identify the y-intercept in a linear equation?

4. Where is the *b* always found on a graph?

## Assessments -

**Do Now:**This will act as an assessment from the pervious lesson. It will be given to the students as they walk into the class and then collected. It will be returned to the students the following day with a grade from 1-4. When the slip is returned we will go over it as a class.

**Homework Check:** I will be walking around the classroom checking students work while they are marking their own work, using the answer I have displayed on the SMART Board. Once they have finish they will have the opportunity to ask question or have specific problems explained. If no one has any questions I will address two or three problems that I felt might have given the students a hard time. During this check I might notice a requiring issue that would get addressed during this time as well.

**Lesson assessment:** During the independent work time and group work time I will be circulating the classroom with a student monitoring check list. This will be used to assess the students immediate understanding of the skill. During these times I will also be sitting down with each table answering and clarifying any further questions the students might have.

**Conclusion:** At the end of the lesson students will come back together as a class. During the share out I will have the opportunity to ask essential questions to determine whether or not the learning target was met.

**Homework:** the students will receive a worksheet, which will be a continuation of the problems done in class

## Lesson-

** Mini Lesson:**

Using a SMARTBoard I will explain what a linear function and equation is. The class and I will take some given equations and move them into a chart creating examples of linear equations and non linear equations. This will get the students actively involved in the lesson by allowing them to come up to the SMARTBoard and move the examples themselves. Next I will identify the y-intercept in a linear equation and demonstrate how the y-intercept of a line is found on a graph. Using the SMARTBoard and a graphing program the students will have the opportunity to see multiple different equations using the same y-intercept. As a class we will be identify the similarities, differences and interesting facts we notice about each graph. There will be four follow up examples. The students will be instructed to find the y-intercept of each using the think-pair-share method. I will encourage each student to think about what their answer is, then share and compare with the people at their tables. Last we will come back as a class to confirm the correct answers.

__I__** ndependent Work: **The student will be given a worksheet which will prompt them to find the slope and y-intercept of each graphed line. The SETTS students will be at one table working with the teacher who pushes in to the class. There is at least one higher level student at each table who will be encouraged to work with the lower levels when any problems arise. I will be circulating the room, answer as many questions as possible and clarify any problems. Circulating and sitting down with each table will also allow me to monitor the student’s progress with the lesson and determine whether or not the learning target was met.

At the conclusion of the lesson, students will come back together as a class and will have the opportunity to share any interesting discoveries they found during the independent work time.

** **** Vocabulary:** During the lesson the students will be given the definitions of the following words, as well as examples of each.

*Linear function, Linear Equations, y-intercept*. These words will be transferred to their vocabulary section at the end of the week.

__Materials__:** **Guided notes via SMARTBoard will assist me in the presentation of the mini lesson. The students will be given handouts that will include any and all graph they need for the lesson. Each student will be provided with a calculator.