<PRE><B>Question 1187922</B>
&lt;br&gt;
Informally....&lt;br&gt;
The additional 35-20=15 guests cost an additional $775-$550=$225, so the cost per guest is $225/15 = $15.&lt;br&gt;
Since the cost for 20 guests is $550, the rental fee is $550-20($15)=$550-$300=$250.&lt;br&gt;
So the rental cost is a fee of $250 plus $15 per guest.&lt;br&gt;
Using formal algebra -- note that the calculations performed are exactly the same....&lt;br&gt;
(x(1),y(1))=(20,550)
(x(2),y(2))=(35,775)&lt;br&gt;
The slope m (increase in cost (y) per guest (x)) is&lt;br&gt;
{{{m = (y(2)-y(1))/(x(2)-x(1)) = (775-550)/(35-20) = 225/15 = 15}}}&lt;br&gt;
The equation is of the form {{{y=mx+b}}}; and we know the slope m is 15.  Plug in (x,y) = (20,550) to find b.&lt;br&gt;
{{{550 = 15(20)+b}}}
{{{550 = 300+b}}}
{{{b=250}}}&lt;br&gt;
ANSWER: The equation for the total cost C for N guests is&lt;br&gt;
{{{C=15N+250}}}&lt;br&gt;
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