Question 164010
We can also use slope-intercept form to prove the above eqn
{{{Y[2]-Y[1]=m(X[2]-X[1])}}}
where,
{{{Y=Fahrenheit}}} ---{{{system(Y[2]=boiling=212F,Y[1]=freezing=32F)}}}
{{{X=Celsius}}} --- {{{system(X[2]=boiling=(100^o)C,X[1]=freezing=(0^o)C)}}}
Substituting,
{{{212-32=m(100-0)}}}
{{{180=m(100)}}} ----> {{{180/100=m*cross(100)/cross(100)}}}
{{{highlight(m=1.8=9/5)}}}
So, {{{Y[1]}}} & {{{X[1]}}} given, and designate {{{Y[2]=F}}}. Also {{{X[2]=C}}}
it follows,
{{{F-32=(9/5)(C-0)}}}
{{{F-32=(9/5)(C)}}}
{{{(F-32)/(9/5)=cross(9/5)C/cross(9/5)}}}
{{{highlight(C=(5/9)(F-32))}}}
Also,
{{{(F-32)=(9/5)(C-0)}}}, transpose to right term "32" fo find {{{F}}}
{{{highlight(F=(9/5)(C)+32)}}}
Thank you,
Jojo</pre>