Education Technology

Linear Equations for Which the Quotient of the Coordinates is Constant

Published on 08/01/2007

Activity Overview

This activity allows students to explore situations in which points with a constant quotient of coordinates are graphed. With TI-Navigator?s display, students can determine that an oblique line is formed from such points. This oblique line always passes through the origin with a slope equal to either the constant quotient or its reciprocal. 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

Before the Activity create a Learning Check that has the questions: If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, what kind of line is it?) Horizontal Oblique Vertical If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, its graph has a y-intercept of ____ and a slope of ____. If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, its graph passes through which quadrant(s)? Quadrant 1 Quadrant 2 Quadrant 3 Quadrant 4 Start TI-Navigator and begin the class.

During the Activity

See the attachment.

After the Activity

Send a Learning Check file to the class to check for their understanding. The first question is a multiple choice one. If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, what kind of line is it? Horizontal Oblique Vertical The second question is a fill-in-the-blank type. If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, its graph has a y-intercept of ____ and a slope of ____. The third question is a multiple choice one for which there is more than one correct answer. If a line has points for which the quotient of the x-coordinate and the y-coordinate is -4, 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.