3.3 Rate of Change and Slope 10/17/18 HW P. 177(4- 12 )

CC State Standards F.IF.6 Calculate and interpret the average rate of change of a function over a specific interval.

Rate of Change Rate of change is a ratio that describes, on average, how much one quantity changes with respect to a change in another quantity. If X is the independent variable (The variable in a function with a value that is subject to choice) and Y is the dependent variable (The variable in a relation with a value that depends on the value of the independent variable). Rate of change = Change in Y Change in X

Find the Rate of Change Rate of change = change in Y (Dollars) Number of Computer Games Total Cost in Dollars X Y 2 78 4 156 6 234 Rate of change = change in Y (Dollars) change in X (Games) = Change in cost Change in number of games = 156 – 78 4 - 2 78 or 39 2 1 Look for patterns and useful information to find the rate of change.

Find the Rate of Change Find the rate of change. Number of Floor Tiles Area of Tiled Surface (in2) X Y 3 48 6 96 9 144 Find the rate of change. Change in Y (Tile Surface) = Change in X (Floor Tiles)

Constant Rates of Change Constant Rates of Change. If the rate of change is constant thus the function is linear. X Y 1 -6 4 -8 7 -10 10 -12 13 -14 X Y - 3 10 - 1 12 1 16 3 18 5 22 Change of Y Change of X

Find the Slope The slope of a non-vertical line is the ratio of the change of the y-coordinates (rise) to the change in the x-coordinate (run) as you move from one point to another. Formula used to find the slope: m(slope)= y2 – y1 x2 – x1 Then label the x and y’s. (3, 6), (4, 8) x1 y1 x1 y2 Substitute the order pairs in the slope formula

Find the slope using the slope formula (-4, - 2) , (0, - 2) Label the x an y’s then put in the slope formula. y2 – y1 x2 – x1 M= (-4, 2) , (-2 , 10) Label and put in slope formula. M=

Find the value of r so the line that passes through each pair of points has the given slope. (6, 8) , (r, - 2), m = 1 Label the x and y’s then put in slope formula. M= y2 – y1 x2 – x1 1 = -2 – 8 r – 6 Simplify 1 = -10 Use cross products r – 6 = -10 Solve for “r.”

Find the value of r so the line that passes through each pair of points has the given slope. (-1, - 3), (7, r) m = ¾ Label x and y’s then put in slope formula (2, 8), (r, -4) m = - 3 Label x and y’s then put in slope formula.

TOTD Find the slope using the slope formula. (14, -8), (7, -6)