<p>Grid ins:
If x, y, and z are positive integers and z=45x-60y, what is the least possible value of x?</p>
<p>The next one is:
In the xy-plane, point A has coordinates (1,0) and point B has the coordinates (11,b). If the slope of line segment AB is greater than 0.5 and less than 0.6, what is a possible vale of b?</p>
<p>First question:z = 45x-60y</p>
<p>And x, y, z all have to be positive integers. Therefore, we will assume the lowest positive value for x, and set the other two values accordingly, and move ascendingly.</p>
<p>If we set x, and y, for 1, then the result of z will be -15, which is negative. No.</p>
<p>If we set x for 2, y for 1, then the result of z will be 30, which is positive. Works!</p>
<p>Therefore, the least possible value of x is 2.</p>
<p>Second question: Simply pick a value between 0.5 and 0.6, and solve for <em>b</em> through the slope forumla.</p>
<p>m = b - 0 / 11-1 = 0.55</p>
<p>b = 5.5</p>