Drill #57 Write an equation in function notation for the following relations: 1.2. 3. {(-1, 6), (0, 3), (1,0)} XY 0-2 10 22 34 XY 6 10 014 118.

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Presentation transcript:

Drill #57 Write an equation in function notation for the following relations: {(-1, 6), (0, 3), (1,0)} XY XY

Drill #58 Find the slope of the line that passes through each pair of points: 1.( 2, 4 ), ( 3, 4 ) 2.( 6, 7 ), ( 4, 8 ) 3.( -9, 3 ), ( -3, 7 ) 4.( 2, -4), ( 2, -8 )

4-1 Rate of Change and Slope Objective: To use rate of change to solve problems and to find the slope of a line. Open books to page 187.

(1.) Rate of Change** Definition: A ratio that describes, on average, how much one quantity changes with respect to another quantity.

Rate of Change Examples Ex1: Real World Example 1A, 1B: Check your progress Ex2: Real World Example 2: Check your progress

(2.) Slope ** The ratio of rise over run in line. The ratio of vertical change to or the horizontal change The ratio of the change in y to the change in x + Rise + Run + Slope - Rise - Slope

(3.) Rise and (4.) Run (3.) Rise: The vertical change, or change in the y-coordinate between two points. (4.) Run: The horizontal change, or change in the x-coordinate between two points. Slope is the ratio of rise and run between two points.

Positive, Negative, Zero, and Undefined (pg 191) (5.) Positive Slope: A line with positive slope rises from left to right (6.) Negative Slope: A line with negative slope goes down from left to right (7.) Zero Slope: A line with zero slope is horizontal (8.) Undefined Slope: A line with undefined slope is vertical

Find the slope of a line Use the rise and the run to find the slope of the following points: 4-1 Practice #1 -4

Formula for Slope (Given Two Points)* Given the coordinates of two points, and, on a line, the slope m can be found as follows:, where

Example of Slope* The slope m of a line is the ratio of the change in the y-coordinates to the corresponding change in the x-coordinates Example: (1,1) (3,2) (5,3)

Find the value of r * Ex: Use the definition of slope to determine the value of r so that the line through ( r, 6) and ( 2, 4) has a slope of 2.

Find the value of r* Ex: Determine the value of r so that the line through ( r, 6) and ( 2, 4) has a slope of 2. m = Method 1 Method 2 (x1, y1) = (2, 4) (x1, y1) = (r, 6) (x2, y2) = (r, 6) (x2, y2) = (2, 4)

Find the value of r Determine the value of r so that the line passing through each pair of points has the given slope: CW.(5, 7), (6, r), m = 3 CW.(6, -2), (r, -6), m = -4