Question 1099748
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I'm assuming this function is linear. If so, then we first need the slope


Slope Formula:


{{{m = (y[2]-y[1])/(x[2]-x[1])}}}


{{{m = (4-(-5))/(3-0)}}} Plug in (x1,y1) = (0,-5) and (x2,y2) = (3,4)


{{{m = (4+5)/(3-0)}}}


{{{m = (9)/(3)}}}


{{{m = 3}}}


The slope is 3


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Use one of the points -- say (x,y) = (0,-5) -- and the slope m = 3 to find the y intercept b


{{{y = mx+b}}}


{{{-5 = 3*0+b}}} Plug in m = 3, x = 0, y = -5


{{{-5 = 0+b}}}


{{{-5 = b}}}


{{{b = -5}}}


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The slope is {{{m = 3}}}. The y intercept is {{{b = -5}}}


Therefore {{{y = mx+b}}} turns into {{{y = 3x+(-5)}}} which simplifies to {{{y = 3x-5}}}


Replace y with f(x) and we have this final answer {{{f(x) = 3x-5}}}
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