4 3 THE SLOPE OF A LINE VOCABULARY

4. 3 THE SLOPE OF A LINE

VOCABULARY Vertical rise – the vertical change of two coordinate pairs Horizontal run – the horizontal change of two coordinate pairs Slope – the ratio of the vertical rise to the horizontal run between any two points on the line

Slopes can be gentle and gradual where the vertical change (rise) is small compared to the horizontal change (run). Slopes can be moderate where the vertical change(rise) is similar to the horizontal change (run). Slopes can be steep where the vertical change (rise) is large compared to the horizontal change (run).

To find the slope of a line, divide the change in the height by the change in the distance traveled. B rise A run Slope AB = rise run To find the slope of line AB: 1) Choose the point farthest to the left and count how many spaces it takes to get to go up to point B. Since point B is 7 spaces above point A, the vertical rise is positive 7. 2) Next, again choose the point farthest to the left and count how many spaces it takes to get to point B. Since point B is 13 spaces to the right of point A, the run is positive 13. The slope of the line AB is rise = 7 run 13

EXAMPLE Notice that since point 2 is below point 1, the vertical change is negative, (-3) Point 1 CCC Point 2 D Also since point 2 is right of point 1, the horizontal change is positive, (+11) To find the slope choose any two points that cross both axes at one point. Next find the vertical change from the point on the left to the point on the right. Then find the horizontal change from the point on the left to the point on the right. The slope is the vertical change divided by the horizontal change. Slope CD = -3 11 No matter what 2 points you choose on line CD, the slope will always be -3 11

SLOPES OF LINES A line with a positive slope rises from the left to the right. A line with zero slope is horizontal (no vertical change). A line with a negative slope falls from the left to the right. A line with undefined slope is vertical (no horizontal change). Since the horizontal change is zero, this makes the denominator of the slope ratio zero AND we all know that division by zero is MEANINGLESS! rise = 4 meaningless run 0 or undefined