Madilyn Quinn
2022-10-17
Answered

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

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rcampas4i

Answered 2022-10-18
Author has **22** answers

We know that the general form of the equation of a linear function is

$$f(x)=ax+b$$

Two points on the linear function are given

Given one point $$(x,y)=(-1,4)\phantom{\rule{0ex}{0ex}}\Rightarrow x=-1,\text{}y=4$$

Put $$x=-1$$ and $$y=f(x)=4$$ in

we get $$4=a(-1)+b\phantom{\rule{0ex}{0ex}}\Rightarrow 4=-a+b\phantom{\rule{0ex}{0ex}}\Rightarrow b=a+4$$

Another point is $$(x,y)=(2,-5)\phantom{\rule{0ex}{0ex}}\Rightarrow x=2,y=-5$$

We get $$-5=a(2)+b\phantom{\rule{0ex}{0ex}}-5=2a+b\phantom{\rule{0ex}{0ex}}-5=2a+a+4\phantom{\rule{0ex}{0ex}}-5-4=3a\phantom{\rule{0ex}{0ex}}3a=-9\Rightarrow a=\frac{-9}{3}\phantom{\rule{0ex}{0ex}}a=-3\phantom{\rule{0ex}{0ex}}\Rightarrow b=-3+4=1\phantom{\rule{0ex}{0ex}}\Rightarrow b=1$$

Required equation of the linear function is $$f(x)=-3x+1$$

$$f(x)=ax+b$$

Two points on the linear function are given

Given one point $$(x,y)=(-1,4)\phantom{\rule{0ex}{0ex}}\Rightarrow x=-1,\text{}y=4$$

Put $$x=-1$$ and $$y=f(x)=4$$ in

we get $$4=a(-1)+b\phantom{\rule{0ex}{0ex}}\Rightarrow 4=-a+b\phantom{\rule{0ex}{0ex}}\Rightarrow b=a+4$$

Another point is $$(x,y)=(2,-5)\phantom{\rule{0ex}{0ex}}\Rightarrow x=2,y=-5$$

We get $$-5=a(2)+b\phantom{\rule{0ex}{0ex}}-5=2a+b\phantom{\rule{0ex}{0ex}}-5=2a+a+4\phantom{\rule{0ex}{0ex}}-5-4=3a\phantom{\rule{0ex}{0ex}}3a=-9\Rightarrow a=\frac{-9}{3}\phantom{\rule{0ex}{0ex}}a=-3\phantom{\rule{0ex}{0ex}}\Rightarrow b=-3+4=1\phantom{\rule{0ex}{0ex}}\Rightarrow b=1$$

Required equation of the linear function is $$f(x)=-3x+1$$

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