# Determine the equation of a linear function that contains the points (-1.4) and (2.-5).

Determine the equation of a linear function that contains the points (-1.4) and (2.-5).
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rcampas4i
We know that the general form of the equation of a linear function is
$f\left(x\right)=ax+b$
Two points on the linear function are given
Given one point
Put $x=-1$ and $y=f\left(x\right)=4$ in
we get $4=a\left(-1\right)+b\phantom{\rule{0ex}{0ex}}⇒4=-a+b\phantom{\rule{0ex}{0ex}}⇒b=a+4$
Another point is $\left(x,y\right)=\left(2,-5\right)\phantom{\rule{0ex}{0ex}}⇒x=2,y=-5$
We get $-5=a\left(2\right)+b\phantom{\rule{0ex}{0ex}}-5=2a+b\phantom{\rule{0ex}{0ex}}-5=2a+a+4\phantom{\rule{0ex}{0ex}}-5-4=3a\phantom{\rule{0ex}{0ex}}3a=-9⇒a=\frac{-9}{3}\phantom{\rule{0ex}{0ex}}a=-3\phantom{\rule{0ex}{0ex}}⇒b=-3+4=1\phantom{\rule{0ex}{0ex}}⇒b=1$
Required equation of the linear function is $f\left(x\right)=-3x+1$