Rate of Change and Slope Monday, November 1, 2010.

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Presentation transcript:

Rate of Change and Slope Monday, November 1, 2010

Definition Rate of change allows you to see the relationship between two quantities that are changing.

Formula Rate of change =

Finding the Rate of Change Using a Table Cost of Renting a Computer Number of Days Rental Charge 1$60 2$75 3$90 4$105 5$120 Rate of change = The rate of change is $15 per day after the first day of rental.

Finding Rate of Change Using a Graph Rate of change = Use two points Divide Simplify

Slope Formula Slope = = where x 2 – x 1 0

Find Slope Using Two Points Slope = Find the slope of the line through A(-2, 1) and B (5, 7). the slope of Line AB is

Find the slope of the line through each pair of points. C (2, 5) and D (4, 7) – Slope is 1. P (-1, 4) and Q (3, -2) – Slope is

Horizontal and Vertical Lines Slope = Substitute two points The slope of a horizontal line is 0.

Slope = Substitute two points The slope of the vertical line is undefined.

Find the slope of the line. Slope = 0

Find the slope of the line. Slope = undefined

Find the slope of the line. Slope = undefined

Find the slope of the line. Slope = 0

Closure What are two ways to find the slope of a line? – You can count the units of rise and run between two points on graph. Or you can find the difference of the y-coordinates, and, in the same order, the difference of the x-coordinates. Then write the quotient of the difference of the y-coordinates divided by the difference of the x-coordinates.