The slope of a line is a measurement of how steep the line is. Another definition is "rise over run." There must be an incline or decline represented by the line to measure steepness. If the line is perfectly vertical, its slope is said to be undefined. If the line is perfectly horizontal, it has a zero slope. You can determine slope if you have an equation for a line, or if you have the coordinates for two or more points on the line.
Linear equations appear in various forms. One form is known as standard form and its format is AX + BY = C. Another common form is slope intercept form. This form presents a line as y = mx + b. Consider the following line: 2X + Y = 8 or y = -2x + 8. This is the same line presented in both forms. The slope of a line is represented by the coefficient of x. In this case, the coefficient of x is -2.
If you have the coordinates for at least two points on a line, you can calculate the slope. Consider the following example points: (3, 4) and (1, 3). The first number in each pair is the x coordinate and the second number is the y coordinate. Subtract y2 from y1 to get 1. Subtract x2 from x 1 to get 2. Place the y data over the x data in a fraction to find the slope. In this example, you write the fraction 1/2. This means that the line rises 1 unit (vertically) whenever it runs 2 units (horizontally).
A line can have either a negative or a positive slope. If a line has a positive slope, then it heads upward in a slant from left to right. If it has a negative slope, then it falls downward in a slant from left to right. A positive slope would look like / and a negative slope would look like \ . If the slope is positive, then the slope data has a plus sign or no sign in front of it. For instance, y = 3x -4 has a positive slope. In contrast a line with a negative slope has a minus sign preceding the slope term, such as in the case of y = -3x -4.