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 determine what the slope (m) is and what the y-intercept (b) is. I will be able to identify whether a given graph model is linear and if it is linear they should be able to write a linear equation in the form y = mx + b that represents the graph model .
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 Ex. Looking at the picture below, we see that we have to move 4 units upward from the point to the left and 6 units over to the right to get to the point on the left. As mentioned before, the slope is rise over run so the slope of the line would be 4/6 = 2/3 . Note that we can choose any two points on the line that have x and y coordinate values as whole numbers. Rise / Run = Up / Over
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