SE: Exploration Guide: Slope - Activity A

Finding Slope

Vocabulary:Coordinates, line graph, negative relationship, points, positive relationship, scale, rise, variable, run, horizontal, vertical, X, Y, ratio, computation, slope, parallel.

Prior Knowledge Questions:

  1. What graphs have you used?
  1. Where have you seen graphs?
  1. Which of these graphs show a positive slope?

Gizmo Warm-up:

There are four sliders in the Gizmotm. This allows you to set the x- and y-coordinates of two different points. Test that out.

The graph at the right of the Gizmo displays (shows) these two points and the line that passes through them. Which two points does the graph show?

Turn on Show rise and run. The rise is the vertical change between two points on a line.

1.Move the x1, y1, x2, and y2 sliders back and forth. Which sliders affect the rise?

2.How might you use the values of these sliders to find the rise between the two points shown on the graph?

3.Without using the Gizmo, try to find the rise between the two points (−1, −3) and (5, 4) on a line.

-1.Check your answer by graphing these points in the Gizmo.

True or False:The rise is also the change along the Y-axis.

Make sure that Show rise and run is turned on. The run is the horizontal change between two points on a line.

4.Move the x1, y1, x2, and y2 sliders back and forth. Which sliders affect the run?

5.How would you use the values of these sliders to find the run between the two points shown on the graph?

6.Without using the Gizmo, try to find the run between the two points (−2, −4) and (4, 3) on a line. Check your answers by graphing these points in the Gizmo. Use the same graphing paper.

7.The rise relates to the ____ axis. The run relates to the ___ axis.

Activity A:
The slope of a line = The ratio between the rise and run. / Get the Gizmo ready:
  • To calculate slope, you divide the rise by the run.
  • Turn on Show rise and run.
/

8.The slope of a line is the ratio between rise and run. Use the sliders to set x1 = −5, y1 = 5, x2 = 3, and y2 = −3.

-1.What are the coordinates of the red point displayed in the Gizmo? What are the coordinates of the blue point?

-1.

-1.What is the rise for these two points? What is the run?

-1.Turn on Show slope computation. What is the slope?

-1.

-1.Look at the graph of the line in the Gizmo. Name two other points that lie on this line.

-1.What are the rise and run for the two points that you chose? What is the slope?

-1.

-1.How does the slope that you just calculated compare to the slope shown for the line in the Gizmo?

-1.

9.Without using the Gizmo, find the slope of a line containing each of the following pairs of points. Then use the Gizmo to check your answers.

-1.(−4, 7) and (4, 1)

-1.(0, 2) and (4, −6)

-1.(−1, −6) and (7, 6)

Exploring Slope

  1. Make sure that Show rise and run and Show slope computation are both turned on. Use the sliders to find a line that goes upward from left to right.
  2. What is the slope of the line that you found? Is the slope positive or negative?
  3. Drag the points to look at other lines that go upward from left to right. What is always true of the slopes of these lines?

4. Drag the points to look at several lines that go downward from left to right? What is always true of the slopes of these lines?

Make sure that Show rise and run and Show slope computation are both turned on. Use the sliders to set y1 = y2 to make a horizontal line. Move the x1 and x2 sliders back and forth.

5. What is the slope of a horizontal line? Does every horizontal line have the same slope? Why?

6. Which axis are all horizontal lines parallel to?

7. Use the sliders to set x1 = x2 to make a vertical line. Move the y1 and y2 sliders back and forth.

8. What is the slope of a vertical line? Does every vertical line have the same slope? Why?

10.Which axis are all vertical lines parallel to?

  1. Use the Gizmo to graph a line containing the points (−4, 2) and (6, 5). Notice that the calculations for rise and run in the Gizmo are Rise = y2 − y1 and Run = x2 − x1.
  1. What is the slope of this line?
  1. What is the result for y1 − y2? How does this result compare to the rise?
  1. What is the result for x1 − x2? How does this result compare to the run?
  1. Divide your result for y1 − y2 by your result for x1 − x2. What number do you get? How does this number compare to the slope for this line?
  1. Based on the calculations that you just performed, do you think it matters which point you use as (x1, y1) and which point you use as (x2, y2) in calculating the slope?