# Linear Equations for Which the Product of the Coordinates is Constant

9-12

# Linear Equations for Which the Product of the Coordinates is Constant

This activity allows students to explore situations in which points with a constant product of x-coordinate and y-coordinate are graphed. With TI-Navigator?s display, students can determine that a curve is formed from such points. This curve is in quadrants 1 and 3 if the product is positive or in quadrants 2 and 4 if the product is negative. The Learning Check enables the teacher to get immediate feedback from the students, thus giving opportunities to correct any errors in understanding.

Before the Activity create a Learning Check that has the questions: If a graph has points for which the product of the x-coordinate and the y-coordinate is -24, what kind of curve is it? Line Curve in one quadrant Curve in two quadrants If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph has either an x-intercept of 24 and a y-intercept of -1 or an x-intercept of -24 and a y-intercept of 1. True False If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph passes through which quadrant(s)? Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Start TI-Navigator and begin the class.

See the attachment

Send a Learning Check file to the class to check for their understanding. The first question is a multiple choice one. If a graph has points for which the product of the x-coordinate and the y-coordinate is -24, what kind of curve is it? Line Curve in one quadrant Curve in two quadrants The second question is a true-false type. If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph has either an x-intercept of 24 and a y-intercept of -1 or an x-intercept of -24 and a y-intercept of 1. True False The third question is a multiple choice one for which there is more than one correct answer. If a curve has points for which the product of the x-coordinate and the y-coordinate is -24, its graph passes through which quadrant(s)? Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Collect the answer files from the classroom. Display the slide show of student responses and discuss the results.

9-12

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