Question 1168508
a linear function {{{g(x)=ax+b}}}

given:

{{{g(1.1)=3.3}}} =>{{{x=1.1}}},{{{g(x)=3.3}}}, that is a point ({{{1.1}}},{{{3.3}}})


{{{g(-2)=7.2}}}=>{{{x=-2}}},{{{g(x)=7.2}}} that is a point ({{{-2}}},{{{7.2}}})


use given points and set system of equations:


{{{g(x)=ax+b}}} ....substitute {{{x=1.1}}},{{{g(x)=3.3}}}

{{{3.3=a*1.1+b}}}........solve for {{{b}}}

{{{3.3-1.1a=b}}}......eq.1


{{{g(x)=ax+b}}} ....substitute {{{x=-2}}},{{{g(x)=7.2}}}

{{{7.2=-2a+b}}}

{{{7.2+2a=b}}}.....eq.2


equal the left sides of eq.1 and eq.2 and solve for {{{a}}}

{{{3.3-1.1a=7.2+2a}}}

{{{3.3-7.2=1.1a+2a}}}

{{{-3.9=3.1a}}}

{{{a=-3.9/3.1}}}

{{{a=-1.258064516129}}}

{{{a=-1.3}}}

go to eq.1 and substitute {{{a}}}

{{{3.3-1.1(-1.26)=b}}}......eq.1

{{{3.3+1.386=b}}}

{{{b=4.686}}}

{{{b=4.7}}}

and your equation is:


{{{g(x)=-1.3x+4.7}}}


check the graph:


{{{ drawing( 600, 600, -10, 10, -10, 10, 
circle(1.1,3.3,.12),circle(-2,7.2,.12),
locate(1.1,3.3,p(1.1,3.3)),locate(-2,7.2,p(-2,7.2)),
 graph( 600, 600, -10, 10, -10, 10, -1.3x+4.7)) }}}