<PRE><B>Question 1203958</B>
&lt;pre&gt;
hello! i need help! i am trying to solve a word problem but i can&#39;t figure it out! the word problem is: &quot;the number of acres of farmland in the US has decreased at a relatively constant rate of 3.27 million acres per year from 1987 to 1997. in 1997, there were 931.8 million acres of farmland.&quot; i have to write an equation that gives the number of acres of farmland as a function of the number of years since 1987. then i have to predict when the number of acres will fall below 915 million acres.

Initial year: 1987, which is treated as YEAR 0. Coordinate point: (0, y&lt;sub&gt;1&lt;/sub&gt;). 
Subsequent year: 1997, which is 10 YEARS after 1987, the initial year. Coordinate point (10, 931.8), or (x&lt;sub&gt;5&lt;/sub&gt;, y&lt;sub&gt;2&lt;/sub&gt;). 

To get your equation, you can use the SLOPE-INTERCEPT form of a linear equation, which is: y = mx + b. Substitute (10, 931.8) for (x, y), and then find the y-intercept, which is also the INITIAL number of acres from the INITIAL year, 
1987

&lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;u&gt;OR&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;/u&gt;  

Simply use the POINT-SLOPE form of a linear equation, which is: 
   &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;y - y&lt;sub&gt;2&lt;/sub&gt; = m(x - x&lt;sub&gt;2&lt;/sub&gt;)&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;  
  y - 931.8 = - 3.27(x - 10) ------ Substituting &lt;font color = blue&gt;&lt;font size = 
4&gt;&lt;b&gt;931.8&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; for &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;y&lt;sub&gt;2,&lt;/sub&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;, - 3.27 for m (slope), and &lt;font color = blue&gt;&lt;font size = 
4&gt;&lt;b&gt;10&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; for &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;x&lt;sub&gt;2&lt;/sub&gt;&lt;/b&gt;
y - 931.8 = - 3.27x + 32.7
        y = - 3.27x + 32.7 + 931.8 ----- Adding 931.8 to both sides
        &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;y = - 3.27x + 964.5&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; &lt;font color = red&gt;&lt;font size = 4&gt;&lt;b&gt;&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;&lt;===== Requested EQUATION&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;

As a prediction is required for the year the number of acres will fall below 915 million acres, 
the requested EQUATION, &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;y = - 3.27x + 964.5&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; becomes the following INEQUALITY:
&lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;- 3.27x + 964.5 &lt; 915&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 
          &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;- 3.27x &lt; 915 - 964.5&lt;/font&gt;&lt;/font&gt;&lt;/b&gt; 
          &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;- 3.27x &lt; - 48.5&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;
                  {{{x &gt; (- 48.5)/(- 3.27)}}} ---- Changing INEQUALITY to its OPPOSITE, since we&#39;re DIVIDING by a negative value 
                  &lt;font color = blue&gt;&lt;font size = 4&gt;&lt;b&gt;x &gt; 15.1376147&lt;/font&gt;&lt;/font&gt;&lt;/b&gt;.
With x being greater than (&gt;) 15.1376147, x = 16 years. So, predicted year after 1987 that the number of acres
will fall below 915 million acres is 2003 (1987 + 16).

You can do the CHECK!!&lt;/pre&gt;</PRE>