The slope of a line measures the dependent variable’s change that’s associated with a change in the independent variable. The dependent variable is the y-variable, and the independent variable is x-variable. So, the equation for the slope, which is represented by an m, of a line is:
In the above equation, the Δ is a Greek symbol which means the change in. You would read the above equation as the change in y divided by the Δx. To find the change in x and the Δy select two points on the graph and calculate the difference between them. That makes the equation for the slope of a line is:
Take the following figure as an example:
The two coordinates for our graph are (3, 4) and (-3, 0). It doesn’t matter which of the two points we choose Point 1 and Point 2. But once we have made that decision, we have to keep with that decision until we find the slope of the line.
For example, we are going to chose (3, 4) as Point 1 and (-3, 0) as Point 2. That makes y2 = 0, y1 = 4, x2 = -3 and x1 = 3. Plugging those values into the slope equation yields:
Subtracting the two values in the numerator and the two values in the denominator.
Since both of the terms are negative, they cancel each other out.
Both of the terms are multiples of 2 so, dividing the numerator and denominator gives us the value of our slope.
If we chose the opposite points for Point 1 and Point 2 That would make y2 = 4, y1 = 0, x2 = 3 and x1 = -3. Plugging those values into the slope equation yields:
4 minus 0 is 4, and 3 minus -3 is 6.
Both of these terms are multiples of 2, so we can divide both the numerator and the denominator by 2 gives us the slope of the line.
Both ways to calculate the slope of a line yields the same result.