Question 1151266

first recall:

{{{Partial}}}{{{ variation }}}is a relationship between two variables in which the dependent variable is the sum of a constant (NOT ZERO) and a constant multiple of the independent variable.

{{{y = mx + b}}}  where {{{b}}} is the initial value of {{{y}}} or {{{y}}}- intercept, and{{{ m}}} is a slope- the constant of variation (what {{{y}}} increases by when {{{x}}}  increases by {{{1}}})

example:
 
A student is eating an ice cream cone at the park that is {{{12.7cm}}} tall. It is extremely hot outside and the ice cream starts to melt at a constant rate of {{{2(cm/min)}}}. If the student didn’t eat any of the ice cream and it started to melt, how much would be left after {{{3}}} minutes? 

1st: Identify the slope and {{{y}}}- intercept

ice cream is melting {{{2(cm/min)}}}, so {{{ m=-2}}}(slope is negative because it is decreasing in size) 

{{{b=12.7}}}

2nd: Plug into slope intercept form:
  
{{{y=-2x+12.7}}} 

3rd: Plug in {{{3}}} for {{{x}}} since we want to know how tall it will be after {{{3}}} minutes 

{{{y=-2*3+12.7}}}
 
4th: Solve 

{{{y=-2*3+12.7 }}}

{{{y=-6+12.7 }}}

{{{y=6.7 }}} cm

Understand that after {{{3}}} minutes of melting the ice cream cone will now measure {{{6.7cm}}}.