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 11 months ago
For a linear function, f(1) = 8 and f(7) = 10. If f(k) = 5, what is the value of k?
 11 months ago
For a linear function, f(1) = 8 and f(7) = 10. If f(k) = 5, what is the value of k?

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campbell_st
 11 months ago
Best ResponseYou've already chosen the best response.1the 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...?

campbell_st
 11 months ago
Best ResponseYou've already chosen the best response.1oops... you need to find the equation before you can find k

myininaya
 11 months ago
Best ResponseYou've already chosen the best response.3Or you could solve the following for k instead of finding the equation of a line: \[\frac{f(7)f(1)}{71}=\frac{f(k)f(1)}{k1}\]

jdoe0001
 11 months ago
Best ResponseYou've already chosen the best response.1\(\bf f(1) = 8 \implies (1,8) \qquad f(7) = 10\implies (7,10) \\ \quad \\ \quad \\ \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ &({\color{red}{ 1}}\quad ,&{\color{blue}{ 8}})\quad &({\color{red}{ 7}}\quad ,&{\color{blue}{ 10}}) \end{array} \\\quad \\ slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}{\color{blue}{ y_1}}}{{\color{red}{ x_2}}{\color{red}{ x_1}}} \\ \quad \\ y{\color{blue}{ y_1}}={\color{green}{ m}}(x{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \qquad \uparrow\\ \textit{pointslope form} \)

jdoe0001
 11 months ago
Best ResponseYou've already chosen the best response.1f(k) = 5 > (k, 5) or "what is the value of "x" if y=5"?
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