The Difference in a No Slope & a Slope of Zero

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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.

Zero Slope

  • 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.

No Slope

  • 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.

Measuring Slope

  • 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.

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