Linear Functions Lesson 1: Slope of a Line

Today’s Objectives Demonstrate an understanding of slope with respect to: rise and run; rate of change; and line segments and lines, including: Determine the slope of a line or line segment using rise and run Classify a line as having either positive or negative slope Explain the slope of a horizontal or vertical line Explain why the slope can be found using any two points on the graph of the line or line Draw a line segment given its slope and a point on the line

Vocabulary Slope The measure of a lines steepness (vertical change/horizontal change) Rise The vertical change of a line Run The horizontal change of a line

Slope of a Line

A)Counting B)Slope formula A (-2,1) B(4,-2) Down 3 Right 6 Slope = rise/run Slope = -3/6 Slope = -1/2 (x 1,y 1 ) (x 2,y 2 ) Slope = rise/run = y 2 -y 1 /x 2 -x 1 Slope = [-2-1]/[4-(-2)] Slope = -3/6 = -1/2

Slope of a Line If the line segment goes downward from left to right, it will have a negative slope. (rise = negative) If the line segment goes upwards from left to right, it will have a positive slope. (rise = positive) *The steeper the line goes up or down, the greater the slope.

Horizontal and Vertical Lines

Example 1) You do Find the slopes of the following line segments. Which line segment has the steepest (greatest) slope? Graph the line segments. A) A(-1, 7)B(4, -3) B) A(-20, 3)B(-4, -5)

Solutions Slope of line a) = -10/5 = -2Slope of line b) = -8/16 = -1/2 Line segment in a) is steeper than line segment b) (-20,3) (-4,-5) (-1,7) (4,-3)

Finding Unknown Coordinates

Another way to find a second point is to simply count out the rise and the run from the one known point. In this case we can read the slope as -2/7 or 2/-7, so we could find two possible points: (-2, -4) or (12, -8) Known point (5, -6) (12, -8) (-2, -4)

Wall Quiz!

Homework Pg # 4,6,9,10,16,17,20,22,24,26,29