## Chapter 1 - Linear Relations

**Prescribed Learning Outcomes:**

D1 Demonstrate an understanding of linear relations by: recognizing patterns and trends, graphing, creating tables of values, writing equations, interpolating and extrapolating, solving problems.

## Chapter 1 key ideas

- Use both forms of the slope formula to calculate the slope of lines and items.
- Explain the difference between independent and dependent variables and identify the axis each is place on.
- Explain the difference between a direct linear relation and partial linear relations.
- Graph information from a problem.
- Recognize positive and negative slopes.
- Identify when relationships are non-linear.
- Use y = mx and y = mx + b to find the equation of a linear relation.
- Define scatterplot, correlation, line of best fit, and outlier.
- Use a line of best fit to gather information about a relationship between two variables: shape (linear or non-linear), strength (weak or strong), direction (positive or negative), and the existence of outliers.

## 1.1 Linear Relations in Tables and Graphs

In this section you must be able to find the slope of a line. You need to understand the difference between a direct linear relation and a partial linear relation as well as the difference between a positive slope and a negative slope.

Please watch the linear relations video and do page 10 #1-3, page 14 #4-6, page 18 #7-8, page 23 #9-10, page 26 #11-12, and page 28 #1-5.

Please watch the linear relations video and do page 10 #1-3, page 14 #4-6, page 18 #7-8, page 23 #9-10, page 26 #11-12, and page 28 #1-5.

## 1.2 The Equation of a Line

In this section you are introduced to the equation of a direct linear relation and the equation of a partial linear relation. Use the slope and the y-intercept to complete each of them.

Please watch the equation of a line video and do page 33 #1, page 35 #2-4, page 39 #5-6, page 42 #7-9, page 45 #10-12, page 48 #13-14, and page 50 #1-5.

Please watch the equation of a line video and do page 33 #1, page 35 #2-4, page 39 #5-6, page 42 #7-9, page 45 #10-12, page 48 #13-14, and page 50 #1-5.

## 1.3 Scatterplots and Linear Trends

Scatterplots are used to find linear trends in information that does not create a perfect line.

1. Graph the points of information to create the scatterplot

2. Draw a line-of-best-fit through the points on the scatterplot

3. Find the equation for the line-of-best-fit - that is the approximate relationship of the two variables in the scatterplot

Please watch the scatterplot and linear trends video and do page 58 #1-2, page 60 #3-4, page 65 #5-6, and page 68 #1-4.

1. Graph the points of information to create the scatterplot

2. Draw a line-of-best-fit through the points on the scatterplot

3. Find the equation for the line-of-best-fit - that is the approximate relationship of the two variables in the scatterplot

Please watch the scatterplot and linear trends video and do page 58 #1-2, page 60 #3-4, page 65 #5-6, and page 68 #1-4.

## Review for the test

Read the key ideas at the top of this page and ensure that you understand them all.

Mark all of your homework with the answer key in the classroom.

Complete and mark the practice test on page 72.

Mark all of your homework with the answer key in the classroom.

Complete and mark the practice test on page 72.