6-1 Rate of Change and Slope. Definitions An independent variable can take any value, independent of any other variable. (usually “x”) A dependent variable.

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Presentation transcript:

6-1 Rate of Change and Slope

Definitions An independent variable can take any value, independent of any other variable. (usually “x”) A dependent variable depends on the independent variable to take on a value. (usually “y”) A rate of change allows you to see the relationship between two values that are changing and is calculated by

Definitions An independent variable can take any value, independent of any other variable. (usually “x”) A dependent variable depends on the independent value to take on a value. (usually “y”) A rate of change allows you to see the relationship between two values that are changing and is calculated by

Example of R.O.C. Number of DaysRental Charge 1$200 2$225 3$250 4$275 Using the table of rental car charges below, find the rate of change using days 2 and 4 The charge “depends” on the number of days.

Example of R.O.C. Number of DaysRental Charge 1$200 2$225 3$250 4$275 Using the table of rental car charges below, find the rate of change using days 2 and 4

Example of R.O.C. Number of DaysRental Charge 1$200 2$225 3$250 4$275 Using the table of rental car charges below, find the rate of change using days 2 and 4

Example of R.O.C. Number of DaysRental Charge 1$200 2$225 3$250 4$275 Using the table of rental car charges below, find the rate of change using days 2 and 4 $25 per day

Lines The rate of change of a line graphed in the coordinate plane is called the slope of the line.

Lines The rate of change of a line graphed in the coordinate plane is called the slope of the line.

Lines The rate of change of a line graphed in the coordinate plane is called the slope of the line.

Lines The rate of change of a line graphed in the coordinate plane is called the slope of the line. Since y-y would be confusing, we need a way to distinguish between them so we use y 1 and y 2

Lines The rate of change of a line graphed in the coordinate plane is called the slope of the line. Since y-y would be confusing, we need a way to distinguish between them so we use y 1 and y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Example of Slope Find the slope of the line that goes through (-3,1) and (6,-4) x 1 y 1 x 2 y 2

Slopes of Lines positive slope negative slope zero slope y = # undefined no slope x = #

Today’s Assignment P. 312 #1-39 odds