Answer :
Answer:
The slope of the secant line joining (2, 0) and (8, 48) is 8.
Step-by-step explanation:
Let [tex]f(x) = x^{2}-2\cdot x[/tex], from Analytical Geometry we remember that slope of a secant line is defined by:
[tex]m_{sec} = \frac{f(x_{B})-f(x_{A})}{x_{B}-x_{A}}[/tex] (Eq. 1)
Where:
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Initial and final independent variables, dimensionless.
[tex]f(x_{A})[/tex], [tex]f(x_{B})[/tex] - Initial and final dependent variables, dimensionless.
Now we proceed to find the values of each dependent variable:
[tex]x_{A} = 2[/tex]
[tex]f(x_{A}) = 2^{2}-2\cdot (2)[/tex]
[tex]f(x_{A}) = 0[/tex]
[tex]x_{B} = 8[/tex]
[tex]f(x_{B}) = 8^{2}-2\cdot (8)[/tex]
[tex]f(x_{B}) = 48[/tex]
And slope of the secant slope is determined after replacing every variable:
[tex]m_{sec} = \frac{48-0}{8-2}[/tex]
[tex]m_{sec} = 8[/tex]
The slope of the secant line joining (2, 0) and (8, 48) is 8.