Linear Functions & Yellow Bowties

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