Question

Ƒ (4) = -8, ƒ (-3) = 1

write a linear function

Answer 1

f(4) = -8 is another way of saying the point is (4 , -8)

f(-3) = 1 is another way of saying the point is (-3 , 1)

to get the equation of any straight line, we simply need two points off of it, so let's use those two provided

`(\stackrel{x_1}{4}~,~\stackrel{y_1}{-8})\qquad (\stackrel{x_2}{-3}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-8)}}}{\underset{run} {\underset{x_2}{-3}-\underset{x_1}{4}}} \implies \cfrac{1 +8}{-7} \implies \cfrac{ 9 }{ -7 } \implies - \cfrac{9 }{ 7 }`

`\begin{array} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-8)}=\stackrel{m}{- \cfrac{9 }{ 7 }}(x-\stackrel{x_1}{4}) \implies y +8 = - \cfrac{9 }{ 7 } ( x -4) \\\\\\ y+8=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}\implies y=- \cfrac{9 }{ 7 }x+\cfrac{36}{7}-8\implies {\Large \begin{array}{llll} y=- \cfrac{9 }{ 7 }x-\cfrac{20}{7} \end{array}}`