Final answer:
To tell that a graph represents a particular equation, analyze the shape and properties of the graph. The form of the trendline equation can also provide insights. Graphs express equations visually, showing the relationship between variables.
Step-by-step explanation:
To tell that a graph is a representation of a particular equation, you need to analyze the properties and shape of the graph. For instance, a linear equation will produce a graph that is a straight line while a quadratic equation will produce a graph that has a parabolic shape.
One way to analyze a graph is by looking at the equation of its trend line. If the graph produces a straight line, the equation of the trend line typically takes the form of y = mx + b, where m is the slope and b is the y-intercept.
In the context of expressing equations visually, graphs can show the relationship between two variables: one is shown on the horizontal axis and the other on the vertical axis. This allows you to see patterns, comparisons, and trends.
For instance, an economic model can use a graph to show the relationship of two variables and provide an intuitive sense of relationships in the data. The pattern shown by graphs can help in solving equations either algebraically or graphically.
Learn more about Analyzing Graphs