## Using Functions to Model a Linear Relationship

#### Aligned To Common Core Standard:

**Grade 8 Functions** - 8.F.B.4

How to use Functions to Model a Linear Relationship - In middle school, there is one common topic taught to all students, which often becomes the reason why students often get confused. That topic is functions. When students are asked to model a linear relationship using a function, they get confused and don’t seem to understand the requirement of the questions. Questions such as these are often presented as word problems and carry certain terms and variables which are difficult to understand in the beginning. The first thing that needs to be done is determining the slope or the rate of change and the initial value of the y-intercept on a certain problem. Let’s learn that from an example: Suppose Sam has $100, and he is saving $20 per week. His initial value or his y-intercept is $100. This is where he started. Every single week he is adding $20 more into the initial value. $20 is his rate of change or the slope. Putting that into an equation we get: Y = mX + c, Y = 20 X + 100 If this equation was to be presented on a graph, it could be seen that a straight line will be formed as there is a constant rate of change taking place at $20.

### Printable Worksheets And Lessons

- Linear Relationship Equation
Step-by-Step Lesson- Use the table we give you to create an
equation for the linear relationship.

- Guided Lesson - Using
premade graphs and tables we ask you to describe relationships between
variables for us.

- Guided Lesson Explanation
- You will find that understanding the meaning of slope is very
helpful when working on this skill.

- Independent Practice
-A series of four pages of tables and graphs for you to work through.

- Matching Worksheet - Match the table to the equation of the line.

#### Homework Sheets

We give you lines in all types of formats and ask you to find the equation for it.

- Homework 1 - Given this table of values for a line, just pick a set of x values and substitute them into the equation and evaluate to get the y values.
- Homework 2 - The straight line equation is y=mx + b.
- Homework 3 - Where m is the slope and b is the y-intercept.

#### Practice Worksheets

In some cases, we will give you multiple points to examine for overall line structure.

- Practice 1 - Write an equation that models the linear relationship in the table below.
- Practice 2 - Determine the equation of the line from given points.
- Practice 3 - What is the equation from the graph?

#### Math Skill Quizzes

I tried to keep the quizzes true to form with the other materials in this section.