© 2007 by S - Squared, Inc. All Rights Reserved.

Horizontal Run Vertical Rise Definition:Definition: Horizontal Run m = = The ratio of the vertical rise (↕) to the horizontal (↔) run between any 2 points on the line

To determine the type of slope, "read" the line from left to right Rises UP from left to right Climbing UP Sliding DOWN Falls DOWN from left to right Horizontal Line Straight ACROSS Straight UP and DOWN and DOWN Vertical Line

What type of slope does this line have? y x

Run 4 1 st : Pick any 2 points on the line 2 nd : Starting with leftmost point, "rise" up to the same level as 2 nd point "rise" up to the same level as 2 nd point 2 nd : Starting with leftmost point, "rise" up to the same level as 2 nd point "rise" up to the same level as 2 nd point 3 rd : At the location after the rise, "run" across to the 2 nd point The number of units of the "rise" becomes the numerator of the slope m = 3 4 The number of units of the "run" becomes the denominator of the slope Rise 3 Rise 3 Run 4 = SLOPE: y x

What type of slope does this line have? y x

Run 3 1 st : Pick any 2 points on the line 2 nd : Starting with leftmost point, "rise" down to the same level as 2 nd point "rise" down to the same level as 2 nd point 2 nd : Starting with leftmost point, "rise" down to the same level as 2 nd point "rise" down to the same level as 2 nd point 3 rd : At the location after the rise, "run" across to the 2 nd point Since we move downward, we use a negative number to represent the "rise" m = −5 3 Rise −5 Rise −5 Run 3 = SLOPE: y x m = 5 3 −

What type of slope does this line have? y x

Run 3 Run 3 1 st : Pick any 2 points on the line 2 nd : Starting with leftmost point, "rise" up/down to the same level as 2 nd point up/down to the same level as 2 nd point 2 nd : Starting with leftmost point, "rise" up/down to the same level as 2 nd point up/down to the same level as 2 nd point 3 rd : Now, just determine the "run" across to the 2 nd point across to the 2 nd point 3 rd : Now, just determine the "run" across to the 2 nd point across to the 2 nd point Since both points are already on the same level, there is NO "rise." m = 0 3 Rise 0 Rise 0 = SLOPE: y x 0

Run 0 1 st : Pick any 2 points on the line 2 nd : Starting with leftmost point, "rise" up/down to the same level as 2 nd point up/down to the same level as 2 nd point 2 nd : Starting with leftmost point, "rise" up/down to the same level as 2 nd point up/down to the same level as 2 nd point 3 rd : At the location after the rise, "run" across to the 2 nd point Since neither point is the leftmost, start with either one. m = 2 0 Rise 2 Rise 2 Run 0 = SLOPE: y x CANNOT DIVIDE BY ZERO UNDEFINED Since we are already at the 2 nd point, there is NO "run."

RISE RUN 1 st : Pick any 2 points on the line 2 nd : Starting with leftmost point, "rise" up to the same level as 2 nd point "rise" up to the same level as 2 nd point 2 nd : Starting with leftmost point, "rise" up to the same level as 2 nd point "rise" up to the same level as 2 nd point 3 rd : At the location after the rise, "run" across to the 2 nd point m = Rise Run SLOPE: y x Finding the slope of a line from its graph over

Climbing UP Sliding DOWN Straight ACROSS UP and DOWN 4 Types of Slope