How do you find the slope of the secant lines of #f(x)=6.1x^2-9.1x# through the points: x=8 and x=16?

Question

Isabella Ackerman · Accepted Answer

137.3

#f(8)=(6.1)(64)-(9.1)(8)=317.6#. This point is (8, 317.6). #f(16)=(6.1)(256)-(9.1)(16)=1416#. This point is (16, 1416). The slope of the secant line joining these two points =#(1416-317.6)/(16-8)=137.3#

Isaiah Allen · Answer

undefined To find the slope of the secant line of $ f(x) = 6.1x^2 - 9.1x $ through the points $ x = 8 $ and $ x = 16 $, you first need to find the corresponding y-values of the function at these two x-values, and then use the slope formula:

$$ \text{Slope} = \frac{{\text{Change in y}}}{{\text{Change in x}}} $$

Substitute the values into the formula:

$$ \text{Slope} = \frac{{f(16) - f(8)}}{{16 - 8}} $$

Calculate $ f(16) $ and $ f(8) $, then find the difference in y-values, and finally divide it by the difference in x-values to find the slope of the secant line.

Emma Aldridge · Answer

undefined To find the slope of the secant line of $ f(x) = 6.1x^2 - 9.1x $ through the points $ x = 8 $ and $ x = 16 $, you first need to find the corresponding y-coordinates for these x-values by substituting them into the function. Then, use the formula for slope: $ m = \frac{{y_2 - y_1}}{{x_2 - x_1}} $, where $ (x_1, y_1) $ and $ (x_2, y_2) $ are the coordinates of the two points. Substituting the given values into the formula will give you the slope of the secant line.