Here's the question you clicked on:
maddtime
For a linear function, f(1) = 8 and f(7) = -10. If f(k) = 5, what is the value of k?
the basic form is y = mx + b start by finding the slope of the line \[m = \frac{f(7) - f(1)}{7 - 1}\] or \[m = \frac{-10 -8}{7 - 1}\] so whats the slope of the line...?
oops... you need to find the equation before you can find k
Or you could solve the following for k instead of finding the equation of a line: \[\frac{f(7)-f(1)}{7-1}=\frac{f(k)-f(1)}{k-1}\]
\(\bf f(1) = 8 \implies (1,8) \qquad f(7) = -10\implies (7,-10) \\ \quad \\ \quad \\ ---------------------------\\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ &({\color{red}{ 1}}\quad ,&{\color{blue}{ 8}})\quad &({\color{red}{ 7}}\quad ,&{\color{blue}{ -10}}) \end{array} \\\quad \\ slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}} \\ \quad \\ y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \qquad \uparrow\\ \textit{point-slope form} \)
f(k) = 5 -> (k, 5) or "what is the value of "x" if y=5"?