<p>Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points?</p>
<p>Answer is 15</p>
<p>Draw a regular hexagon and see how many ways you can connect the vertices.</p>
<p>Thanks ^. Here’s another:</p>
<p>If x< 0 and x is inversely proportional to y, which of the following is directly proportional to 1/x^2.</p>
<p>Answer is y^2.</p>
<p>What were the other choices?</p>
<p>Inverse proportionality means that as one variable INCREASES the other variable DECREASES, and vice-versa. Direct proportionality means that as one variable INCREASES the other variable INCREASES as well. </p>
<p>You know that when a numerator (the top part of a fraction) increases, the fraction increases; and when a denominator (the bottom part of a fraction) increases, the fraction decreases. So, if X is inversely proportional to Y, then 1/X is directly proportional to Y. You are basically switching X from the numerator (X/1) to the denominator (1/X), thereby changing the proportionality. The question basically asks for this simple understanding. Since X and Y are inversely proportional, they act differently. As one goes up the other goes down; as one goes down the other goes up. Switching X to 1/X changes the relationship with Y to a DIRECT relationship, because as X goes up, 1/X goes down. It flips it…</p>
<p>Algebraically:</p>
<p>Inverse proportionality:
k = xy; k is a constant
As x goes up, y must go down to maintain the constant (e.g., 24 = 1<em>24 = 2</em>12 = 3<em>8 = 4</em>6; the first factor is increasing while the second factor is decreasing).</p>
<p>Direct proportionality:
k = x/y; k is a constant
As x goes up, y must also go up to maintain the constant (e.g., 1/2 = 2/4 = 4/8 = 8/16 = 16/32; both the numerator and the denominator are increasing at the same time).</p>
<p>Thus, since x and y are inversely proportional, k = xy.
k = xy
k/x = y
k/x^2 = y^2
1/x^2 = y^2</p>
<p>(K is just an arbitrary constant. As long as K represents a constant, the relationship stays the same.)</p>
<p>Thanks I get it now :)</p>