Slope of a Line

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1. Click on the above button "click here to start" and maximize the window obtained.
   
   
2. Drag points slowly A (X_{A ,} Y_A) and B (X_{B ,} Y_B) so that the line has a certain position. You can also adjust the coordinates of A and B by first clicking on the points and then use the buttons on the left panel either to increase (+) or decrease (-) x or y coordinate. Use the definition of the slope of a line:
   
   m = (Y_A - Y_B) / (X_A - X_B)
   to find the slope of the line. Check your answer against the value given at the top left.
   
   
3. Change the position of one point so that so the slope is positive. As x moves from the left to the right the line rises, falls or is horizontal?
   
   
4. Change the position of one point so that so the slope is zero. As x moves from the left to the right the line rises, falls or is horizontal? Compare the y coordinates of the two points.
   
   
5. Change the position of one point so that so the slope is negative. As x moves from the left to the right the line rises, falls or is horizontal?
   
   
6. Change the position of two points so that their x coordinates are equal. What is the slope? Explain analytically using the formula. What is the position of the line?
   
   
7. Change the position of the two points such that they have the same coordinates. Is there a line? Can you define a slope?

Slopes of Parallel lines

1. On the left panel, click on the check box "two lines". Two lines are now displayed and you can change their position by dragging points A, B, C and D. Change the position of one line so that the two are parallel ( no point(s) of intersection). Compare the slopes of the lines.

Slopes of Perpendicular lines

1. Change the position of the lines so that they are perpendicular ( make an angle of 90 degrees). To make sure that they are perpendicular, adjust the lines so that they go though the diagonals of the small squares in the rectangular system. Find the product of the two slopes. Do this last experiment several times. What can you say about the product of the slopes of two perpendicular lines?

• Easy to use calculator to find slope and equation of a line through two points.Two Points Calculator
  
  
• Another calculator to find slope, x and y intercepts given the equation of a line.Find Slope and Intercepts of a Line - Calculator