Question 190124
(a) let the years denote the x-coordinates and the consumption of red meat be denoted by the y-coordinates, then we are given the following coordinates:

Since, year 1900 corresponds to x = 0, the year 1970, will correspond to  x = 70. so when x = 70, y = 131.7 pounds. The point can be represented as 
 (70,131.7)
similarly, when year is 2000, then x = (2000 - 1900) = 100. so we have 
 (100, 107.7) as another coordinate in our xy-system.

now since we have two points, using the point-slope formula we can determine the linear equation as:

{{{ y-y[1] = ((y[2] - y[1]) / (x[2] - x[1]) )*(x - x[1]) }}}

{{{ x[1] = 70 }}}
{{{ x[2] = 100 }}}
{{{ y[1] = 131.7 }}}
{{{ y[2] = 107.7 }}}

thus the equation becomes:

{{{ y- 131.7 = ((107.7 - 131.7) / (100 - 70) )*(x - 70) }}}
=> {{{ y - 131.7 = (-30 / 30) * (x - 70) }}}
=> {{{ y - 131.7 = (-1) * (x - 70) }}}
=> {{{ y - 131.7 = -x + 70 }}}
=> {{{ y  = -x + 70 + 131.7 }}}
=> {{{ highlight(y  = -x + 201.7) }}} -- this is the rule.

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(b)
we are given y = 100 pounds, we need to determine that value of x for which y = 100 pounds. We plug this value of y in our equation.

{{{ y  = -x + 201.7 }}}
=> {{{ 100  = -x + 201.7 }}}
=> {{{ x  = 201.7 - 100 }}}
=> {{{ x = 101.7 }}}
we can take x approx as 102. so the year would be {{{ 1900 + 102 = 2002 }}}

Hope this helps.