Graphs
In many situations, the value of one quantity depends on the value of another. It is often easier to understand the relationship between two quantities by looking at a graph that displays the value of one quantity against the value of the other. Graphs also help us to predict trends and to answer "what-if" problems.
Let us consider the relationship between the amount of some product formed in a reaction and the temperature of the reaction. The experiment is designed so that we change the temperature and then measure the amount of product at that temperature. The horizontal axis (x-axis) is used for the quantity that can be controlled or adjusted; in this example, temperature is placed on the horizontal axis. The vertical axis (y-axis) is used for the quantity that responds to changes in the quantity on the x-axis, in this case the amount of product formed. We can say that amount of product depends on temperature; often the quantity on the y-axis is called the dependent variableand the quantity on the x-axis is the independent variable. The experimental data are placed on the graph and connected with a smooth line.
The line connecting the points on a graph can assume many different shapes. A straight-line or linear relationship can be described by an equation such as
y=3x+2
This relationship predicts the value of y for a given value of x. For example, when x is adjusted to have a value of 4, then y will be 14. The general equation of a straight line is
y=mx+b
The quantity b is called the y-intercept, and it provides the value of y when x is equal to 0. The quantity m is called the slope of the line, and it provides information about the degree of slant. Lines with positive values of m slant up toward the right, a line with a value of zero for the slope is level, and lines with negative values of the slope slant down toward the right. The slope is evaluated by measuring the change in the dependent variable (
y) for a given change in the independent variable (x). We represent the change in any variable by using a Greek delta,, which should be understood to mean (final value-initial value).
The slope of a line representing a measured quantity must have units. If, for example, the x-axis is time in seconds and the y-axis is temperature in 