Some people think of neckwear when they hear the word "bowtie"; some think of pasta. [br]In this applet "bowtie" refers to the shape formed by two intersecting linear functions and the lines x = a and x = b.[br][br]Use the white dots to position the bowtie and set the values of a and b.[br]Use the blue and green dots to determine the slopes of the two linear functions.[br][br]What linear functions are the blue and green lines?[br]Where do they intersect?[br]What is area of the "bowtie"?[br]How does the area of the "bowtie" depend on the horizontal position of the intersection point of the two functions? on the vertical position?[br]What are some other questions you can ask your students about this construction?