<p>p 778 in Blue book, number 14 (grid in)</p>
<p>Three distinct points P Q R lie on a line L; the four distinct points S,T,U,V lie on a different line parallel to line L. What is the total number of different lines that can be drawn so that each line contains exactly two of the seven points. </p>
<p>p 805 number 8</p>
<p>In the xy coordinate system, (root 6, k) is one of the points of intersection of the graphs y=(x^2) - 7 and y = -(x^2) + j, where j is a constant. What is the value of j? </p>
<p>A. 5
B. 4
C. 3
D. 2
E. 1</p>
<p>thanks!</p>
<ol>
<li>3 X 4 = 12. </li>
</ol>
<p><-P-Q-R-></p>
<p><-S-T-U-V-> </p>
<p>Just draw lines to make each possibility and you see that it comes out to 3*4 = 12. </p>
<ol>
<li></li>
</ol>
<p>EDIT: I'll clarify this: </p>
<p>In order for the two to "intersect", they must have the same y coordinate. Plug in the x coordinate of the intersection point into the equation without the j so that we're not left with an unknown: </p>
<p>y = ( sqrt(6) ) ^2 - 7 = -1
Since both equations are equal and have the same x coordinate, we can plug in what we know into the equation with the unknown j:
-1 = -(sqrt(6)) ^2 + j
-1 = -6 + j -> j = 5 -> (A)</p>
<p>THANKS~! but for the first one, I accidentally thought that 2 numbers on the same line can go with each other. Why can't that happen?</p>
<p>Because they're already on the same line, so you can't form a new line from points already on the same line...</p>