Final answer:
Students must be familiar with key graph vocabulary such as 'algebraic equation', 'y-intercept', and 'slope', along with understanding the relationships indicated by a line's slope. Recognizing that graphs provide one perspective and being critical of their presentation are also essential skills for interpretation.
Step-by-step explanation:
Understanding the functions of graphs in mathematics is essential for students, especially in subjects like economics where graphs are used to express equations and data visually. One important piece of vocabulary is the algebraic equation of a line, expressed as y = b + mx, where 'y' represents the variable on the vertical axis, 'x' is on the horizontal axis, 'b' is the y-intercept, and 'm' represents the slope of the line. The y-intercept is where the line crosses the vertical axis, and the slope indicates the rate of change between the two variables on the graph. The slope's sign (positive, negative, or zero) conveys the nature of the relationship between these variables.
Moreover, it is crucial for students to approach graphs with a critical eye, understanding that a graph is just one perspective influenced by the choices made in its creation. Critical vocabulary terms that students should be comfortable with include 'positive relationship' when the slope is upward, indicating that as one variable increases, so does the other; 'negative relationship' for a downward slope, where one variable decreases as the other increases; and 'zero slope' which suggests no relationship, showing that the variable on the vertical axis remains constant regardless of the horizontal variable. Mastering this language is key to accurately interpreting and describing the functions of graphs in various contexts.