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Linear Equations Day 1:

Linear Equations Day 1 Eighth Grade Algebra 1 Ms. P erez

Objectives:

Objectives Throughout this unit: I will learn what a linear equation is and how it is often written as y = mx + b. I will be able to identify whether a given model is linear and if it is linear, I will be able to determine what the slope (m) is and what the y-intercept (b) is.

Before Starting the Lesson:

Before Starting the Lesson On your worksheet, answer the following question: 1. What do you think a linear equation is? As a class, lets share what we think a linear equation is.

What is a linear equation?:

What is a linear equation? A linear equation is an equation that makes a straight line when it is graphed. Linear equations are often written in the form, y = mx + b, known as the slope-intercept form , where m is the slope and b is the y-intercept. (Note: Throughout this unit, we will only focus on linear equations of the form y = mx + b)

The slope (m) part of y = mx + b:

The slope (m) part of y = mx + b The slope (m) is the measure of the steepness of a line or a section of a line connecting two points. When finding the slope from a line, we use m = slope = rise over run or the change in y over the change in x , where slope is represented by m . In word problems, the slope is often referred as the rate of change (ex. m iles per hour, gallons per minute , etc.)

VIDEO DEMONSTRATION:

VIDEO DEMONSTRATION Click on the link below to watch the short video clip stopping at 2 minutes and 30 seconds: https:// www.youtube.com/watch?v=2kMUk_XRvRQ

Finding the slope from a line:

Finding the slope from a line Looking at the picture below, we see that we have to move 4 units upward from the bottom point and 6 units over to the right to get to the top point. As mentioned before, the slope is rise over run so the slope of the line would be 4/6 = 2/3 .

Try exercises 2 and 3 on your own:

Try exercises 2 and 3 on your own 2 . Find the slope of the line using the given points. 3. Draw a line that passes through points (1, 2) and (-1, 0). What is the slope of the line?

What does it mean to have a positive, negative, zero slope, or an undefined slope graphically?:

What does it mean to have a positive, negative, zero slope, or an undefined slope graphically? Click the link below to watch the “Slope Dude” short video clip below that will answer the question above: https :// www.youtube.com/watch?v=ZcSrJPiQvHQ

Group Discussion :

Group Discussion What does it mean to have a positive or negative slope? Discuss with three other classmates and be ready to share as a class.

The y-intercept (b) part of y = mx + b:

The y-intercept (b) part of y = mx + b The y - intercept of a line is the value of y at the point where the line crosses the y axis . In word problems, the y-intercept is often referred to as the initial or starting point (ex . initial deposit, initial amount , etc.)

Group Collaboration:

Group Collaboration Now that you know to find m and b, within groups of 3 to 4 decide which of the following graphs can be represented by a linear equation and explain why. If it can be represented by a linear equation, write down the linear equation in slope-intercept form that the graph represents. Make sure to show your own work underneath each graph on the worksheet notes.

End of the Lesson:

End of the Lesson

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