Find an equation of the secant line containing (1, f(1)) and (2, f(2)).
-$$f ( x ) = \sqrt { x + 24 }$$
A) $y = ( \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$
B) $y = ( \sqrt { 26 } - 5 ) x + \sqrt { 26 } - 10$
C) $y = ( - \sqrt { 26 } - 5 ) x - \sqrt { 26 } + 10$
D) $y = ( - \sqrt { 26 } + 5 ) x + \sqrt { 26 } - 10$

Question

Quizplus · Accepted Answer

The slope of the secant line is calculated using the points (1, f(1)) and (2, f(2)). First, find f(1) and f(2): $f(1) = \sqrt{1 + 24} = \sqrt{25} = 5$ and $f(2) = \sqrt{2 + 24} = \sqrt{26}$. The slope $m$ is $\frac{f(2) - f(1)}{2 - 1} = \sqrt{26} - 5$. Using point-slope form, $y - f(1) = m(x - 1)$, substitute $f(1) = 5$ and $m = \sqrt{26} - 5$ to get $y - 5 = (\sqrt{26} - 5)(x - 1)$. Simplify to get the equation in the form $y = mx + b$, resulting in $y = (\sqrt{26} - 5)x - \sqrt{26} + 10$.

Find an Equation of the Secant Line Containing (1, F(1)) f(x)=x+24f ( x ) = \sqrt { x + 24 }f(x)=x+24​

Find an Equation of the Secant Line Containing (1, F(1)) $f ( x ) = \sqrt { x + 24 }$