<p>Jodi Gardner, Gary Salo, Tina Marenger, Sarah Hill, Jason Elsenbroek</p><p>Grade Level: 8</p><p>Activity: Exploring Parallel and Perpendicular Lines</p><p>Activity Description: In groups, students will complete two tables and write an equation for each set of data in slope-intercept form. They will graph the equations on transparencies and on chart-size graph paper. The students will compare the two sets of graphs and equations to determine the relationships of the slopes of pairs of lines that are parallel and pairs of lines that are perpendicular.</p><p>Materials Needed: handout for each group, markers, Vis-à-vis markers, transparency sheets with coordinate plane, chart-size graph paper, meter sticks</p><p>Key ideas: Parallel and perpendicular lines, equations.</p><p>Connections to Michigan GLCE’s:</p><p>8th: A 2.4.1: Write the symbolic forms of linear functions (standard [i.e., Ax + By = C, where B 0], point-slope, and slope-intercept) given appropriate information and convert between forms.</p><p>A2.4.4: Find an equation of the line parallel or perpendicular to given line through a given point. Understand and use the facts that nonvertical parallel lines have equal slopes and that nonvertical perpendicular lines have slopes that multiply to give -1.</p><p>Teacher Prompts:</p><p>-Before: All 8th grade students should be familiar with the coordinate plane and graphing. The teacher will review some basic vocabulary pertaining to ordered pairs, quadrants, slope-intercept form, point-slope form, and tabular examples.</p><p>-During: Each group will be given specific directions on the completion of their project. Each group will receive two different examples of linear functions. The pairs of lines will either be parallel or perpendicular. They will complete the table, determine the slope, y-intercept, and the equation for each line. Then they will graph each line on the transparency and on the large graph paper. Students will compare the two lines and their equations to determine the relationship between the two slopes when the lines are either parallel or perpendicular.</p><p>The groups that complete the activity may work on the extension for the activity where students are given a partially-completed table and asked to determine the equation for the line and fill in the missing values for x and y. Group 1</p><p>1. Use this table to write an equation in slope-intercept form. </p><p> x y -3 -11 Slope: ______-2 -9 -1 -7 y-intercept: ______0 -5 1 -3 2 -1 Equation: ______3 1</p><p>2. Use this table to write an equation in slope-intercept form. </p><p> x y Slope: ______-3 2 -2 4 -1 6 y-intercept: ______0 8 1 10 2 12 Equation: ______3 14</p><p>Compare the 2 equations and the graphs. What do you notice? *Graph each equation on an overhead graph sheet as well as on the large graph paper provided. Remember to write the equation next to your line!</p><p>Extension—Group 1</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph.</p><p> x y -3 7 y-intercept: 4 -2 -1 5 Equation: ______1 3</p><p>3 1</p><p>When x has a value of 20, what is the value of y? </p><p>______</p><p>When y has a value of 27, what is the value of x?</p><p>______x y -3 8 -2 5 -1 2 0 -1 1 -4 Group 2 2 -7 3 -10</p><p>3. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______</p><p> x y y-intercept: ______-3 11 -2 8 -1 5 Equation: ______0 2 1 -1 2 -4 3 -7</p><p>4. Use this table to write an equation in slope-intercept form. Slope: ______y-intercept: ______</p><p>Equation: ______</p><p>Compare the 2 equations and the graphs. What do you notice?</p><p>*Graph each equation on an overhead graph sheet as well as on the large graph paper provided. Remember to write the equation next to your line!</p><p>Extension—Group 2</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph.</p><p> x y -3 6.5 y-intercept: 8 -1 7.5</p><p>Equation: ______1 8.5 2 3 9.5</p><p>When x has a value of -22, what is the value of y? ______</p><p>When y has a value of 30, what is the value of x?</p><p>______</p><p> x y -3 17 -2 14 -1 11 0 8 1 5 2 2 3 -1</p><p>Group 3</p><p>5. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______y-intercept: ______Equation: ______</p><p>6. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______y-intercept: ______</p><p>Equation: ______</p><p>Compare the 2 equations and the graphs. What do you notice? x y -3 -5 -2 -4.666666667 *Graph each equation -1 -4.333333333 on an overhead graph 0 -4 1 -3.666666667 sheet as well as on 2 -3.333333333 the large graph paper 3 -3 provided. Remember to write the equation next to your line! Extension—Group 3</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph. x y y-intercept: 4 -3 10 -2 -1 6 Equation: ______1 2</p><p>3 -2</p><p>When x has a value of 26, what is the value of y?</p><p>______</p><p>When y has a value of 40, what is the value of x?</p><p>______</p><p>Group 4 7. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______x y -3 10 y-intercept: ______-2 8 -1 6 0 4 Equation: ______1 2 2 0 3 -2</p><p>8. Use this table to write an equation in slope-intercept form. </p><p> x y -3 6.5 -2 7 Slope: ______-1 7.5 0 8 y-intercept: ______1 8.5 2 9 3 9.5 Equation: ______</p><p>Compare the 2 equations and the graphs. What do you notice? *Graph each equation on an overhead graph sheet as well as on the large graph paper provided. Remember to write the equation next to your line! Extension—Group 4</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph.</p><p> x y -3 8 y-intercept: -1 -2 -1 2 Equation: ______0 2 -7 3 -10</p><p>When x has a value of -16, what is the value of y?</p><p>______</p><p>When y has a value of 26, what is the value of x?</p><p>______x y Group 5 -3 -1.5 -2 0 -1 1.5 0 3 9. Use this table 1 4.5 to 2 6 write an 3 7.5 equation in slope- intercept form. </p><p> x y Slope: ______-3 1 -2 0.333333333 y-intercept: ______-1 -0.333333333 0 -1 1 -1.666666667 Equation: ______2 -2.333333333 3 -3</p><p>10. Use this table to write an equation in slope-intercept form. Slope: ______y-intercept: ______</p><p>Equation: ______</p><p>Compare the 2 equations and the graphs. What do you notice?</p><p>*Graph each equation on an overhead graph sheet as well as on the large graph paper provided. Remember to write the equation next to your line!</p><p>Extension—Group 5</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph.</p><p> x y -3 -11 y-intercept: -5 -9 -1 -7 0 Equation: ______1 -3 -1 3 1</p><p>When x has a value of -15, what is the value of y? ______</p><p>When y has a value of 39, what is the value of x?</p><p>______</p><p> x y -3 7 -2 6 -1 5 0 4 1 3 2 2 3 1</p><p>Group 6</p><p>11. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______y-intercept: ______Equation: ______</p><p>12. Use this table to write an equation in slope-intercept form. </p><p>Slope: ______y-intercept: ______</p><p>Equation: ______</p><p>Compare the 2 equations and the graphs. What do you notice? x y *Graph each -3 0 -2 -1 equation on an -1 -2 overhead graph 0 -3 sheet as well as on the 1 -4 large 2 -5 graph paper 3 -6 provided. Remember to write the equation next to your line!</p><p>Extension—Group 6</p><p>1. You are given a partial table and the y- intercept. From the information given, develop an equation in slope-intercept form and draw the graph. y-intercept: -3 x y -3 -2 Equation: ______-2 0 2 -5 3 -6</p><p>When x has a value of -21, what is the value of y?</p><p>______</p><p>When y has a value of -31, what is the value of x?</p><p>______</p>