Four Kinds of Slope: Uphill, Downhill, Flat and a Wall

0:00Slope measures how steep a line is. There are four kinds of slope.

0:05To find the slope, divide the rise, the change in y, by the run, the change in x.

0:13Read each line from left to right, as if walking along it.

0:17This line goes uphill. It passes through (2, 1) and (4, 5).

0:24The rise is 5 minus 1, which is 4. The run is 4 minus 2, which is 2.

0:324 divided by 2 is 2. Uphill means a positive slope.

0:38This line goes downhill. It passes through (2, 5) and (5, negative 1).

0:45The rise is negative 1 minus 5, which is negative 6. The run is 5 minus 2, which is 3.

0:54Negative 6 divided by 3 is negative 2. Downhill means a negative slope.

1:01This line is flat: you never go up or down. It passes through (1, 3) and (5, 3).

1:09The rise is 3 minus 3, which is 0. The run is 5 minus 1, which is 4.

1:170 divided by 4 is 0. A flat, horizontal line has a slope of zero.

1:24This vertical line goes straight up, like a wall. It passes through (2, negative 1) and (2, 5).

1:33The rise is 5 minus negative 1, which is 6. The run is 2 minus 2, which is 0.

1:416 divided by 0 has no answer, because no number times 0 makes 6. A wall has an undefined slope.

1:50Careful: a vertical line does not have a zero slope. Zero is flat, and vertical is undefined.

1:58Uphill is positive, downhill is negative, flat is zero, and a wall is undefined.