Slope Exploration
Slope is a description of a line's direction and steepness. Explore how the slope of the black line below changes when you move points A and B.
Directions: In the manipulative below, the slope of the black line is being calculated using points A and B. Change the slope of the line by moving points A and B. Try to avoid having decimals in the coordinates of points A and B to make the exploration easier to follow.
Try to answer the following questions:
- How would you describe the black line when the slope is negative and when it is positive?
- Where does the numerator of the slope come from?
- Where does the denominator of the slope come from?
- How is the slope calculated?
Note: The slope shown in the manipulative below may be an unreduced fraction, but when we do our own slope calculations, we want to make sure our fractions are reduced.