The Difference in a No Slope & a Slope of Zero
Lines and angles are an important aspect of measurements for home and garden projects. The slope of a line measures its "steepness," according to Math Open Reference. On a graph, a line with positive slope points upward; its value of y, the vertical line on a graph, increases as the line progresses along the x-axis, the horizontal line on a graph. A line with negative slope points downward; its y-values decrease as the line progresses away from the y-axis. Lines with zero slope and lines with no slope differ from other lines and from one another.
Lines with a slope of zero are horizontal -- completely level or flat -- because all the y-values on the line are the same. When you incorporate the y-values of a horizontal line into the formula for computing the slope of a line, the numerator, or top value of the number in a fraction, is zero. Because of this, it doesn't matter how long the line is, it is always at a 90-degree angle to the y-axis and parallel to the x-axis.
Horizontal lines are essential in constructing level floors, shelves and other flat surfaces within your home. You also use horizontal lines for constructing a deck or porch. These are all surfaces that ideally would be completely flat.
Lines that are vertical are said to have an undefined slope or no slope because the formula for determining slope uses values from the x-axis in the denominator, or bottom value of a fraction. Because the values of the x-axis remain the same with a vertical line, calculating its slope would result in attempting to divide by zero, which is impossible in ordinary geometry or mathematics. On a graph a vertical line would stand at a 90-degree angle from the x-axis and would be parallel to the y-axis.
Vertical lines are important to construction. The walls of a building are ideally perfectly vertical, that is, they stand straight up. Windows should also be vertical to fit properly within the walls in which you install them.
To measure the slope of a line, choose any two points along that line. Note the position of each point along both the x-axis and the y-axis. Record the positions as (x1, y1) for the point closest to the y-axis and (x2, y2) for the point further away from the y-axis. Import the two values into the formula for calculating slope: y1 minus y2 divided by x1 minus x2. If the result is a positive number, the line has a positive slope. If the result is a negative number, the line has a negative slope. You can choose any two points along the line; the formula will produce the same result.