#  >> K-12 >> AP Classes

How to Write Units in Linear Equations

Linear equations are often used to model the change in magnitude of a unit over time, such as miles per hour. The unit is represented by the slope of the line against a variable "x." The standard representation of a linear equation, however, is slightly different than that of a line, which represents value changes over time in a real plot. Specifically, the representation of slope and variable are combined while the representation of "b" (the intercept at the Y axis) is often ignored entirely.

Instructions

    • 1

      Simplify any fraction within the equation. Specifically, ensure that the slope is in its simplest form. For example, taking the function f (x) = 2 / 6 * x + 13, simplifying the fraction yields f (x) = 1 / 3 * x + 13.

    • 2

      Combine the variable and slope into one fraction. Continuing from above, f (x) = 1 / 3 * x + 13 resolves to f (x) = x / 3 + 13. This is a fraction property that exemplifies the fact that something multiplied by 1 / 3 is equal to the same thing divided by 3.

    • 3

      Move all unit names from the denominator into the numerator. In doing this, it is imperative to remember to raise the name of the unit to the negative value of its exponent. Further, if no exponent is present on the unit there is an understood exponent of 1. For example, if this represents 1 dollar per 3 hours worked, where x is the number of hours worked, we would change f (x) = x * dollars / 3 * hours + 13 to f (x) = x * dollars * (3 * hours)^ -1 + 13. This puts the equation into a more compact form using the property of exponents which states that x ^ -1 = 1 / x.

    • 4

      Remove any additional terms added to the function of the slope itself. This step is optional, but most unit graphs are concerned with small segments of time that do not include the Y axis. This removal of additional terms allows for easier manipulation of the equation when required. This has the effect of changing the equation from f (x) = x * dollars * (3 *hours)^-1 + 13 to f (x) = x * dollars * (3 * hours)^ -1. This lost term should not be forgotten, however, in examining its graph and translated values it is unnecessary to continue reiterating it. This is because any plotted point that is used for reference will already have the "+13" value accounted for in its graph position. Therefore, all points plotted before or after using the initial point will have the "+13" value inherently added to their position as well.

Learnify Hub © www.0685.com All Rights Reserved