## Slope.

Another day, another algebraic challenge! Since we learned about Cartesian Coordinate System last time, we’ll take advantage of the knowledge to take further into the world of function!

The slope of a line represents the steepness of the graph and is defined as the rate of change of the y-coordinates of the points on the graph as you move from left to right. The slope is denoted by “m” in the equation of a line. The origin of the symbol “m” is unclear, but one can associate it with “move” to help remember its significance.

### The formula for the slope of a line:

Rise means vertical movement (up and down) and run means

horizontal movement (left and right).

The slope of a line can be calculated by determining the rise (the change in the y-coordinate) and run (the change in the x-coordinate) between two points on the graph and dividing the rise by the run. This can be remembered as “rise over run” because, in a fraction, the numerator is written “over” the denominator.

### Another formula:

(x1, y1) is one point on the line and (x2, y2) is another point on the line.

The algebraic way of finding the slope of a line involves using two points (x1, y1) and (x2, y2) on the line. This method can be used when the graph is not available or when it is difficult to determine the rise and run by examining the graph.

The order in which two points on a line, (x1, y1) and (x2, y2), are used to calculate the slope does not affect the result as the slope of a line is constant. Regardless of which pair of points is used, the slope will always be the same.

## Sample:

What is the slope of the line?

Find two points on the graph and count the rise (up and down) and run (to

the right).

The rise is 3 and the run is 4, so the slope is 3/4.