The value of b in the linear function of f(x) = mx + b refers graphically to the y-intercept of the graph. The y-intercept is the point where the graph crosses the y axis. This means numerically that b is the value of y (on the y axis of the graph) when x = 0. Students may be asked to use this function to graph several different points on the graph by changing the variable m.
In the third grade students begin to learn how to view the multiplication tables that they have been memorizing as function tables. This transition assists students in the understanding of linear function formulas like the one used above and also help to make the associations between ordered pairs and functions more apparent to younger students. While students may not be able to immediately make the correlation between function and multiplication tables, they begin to be taught to understand how constant rates work in third grade.
Third grade students are given simplified versions of the linear equation noted above to begin their understanding of algebraic functions. Some third grade curriculum materials help students to learn linear functions without having to express them algebraically. Where a multiplication table can algebraically be thought to be expressed as y = mx, a third grade student may be taught the same linear function using a multiplication table or "times table." The student can then begin to graph linear functions manually, utilizing both the multiplication table and the introduction of the values of x and y as they correspond to the graph.
Another way in which third grade students are regularly introduced to linear functions and constant rates is through the use of incomplete tables. These tables are often used in conjunction with a word problem. The table presents the information in a way that the student can understand and logically work out how to complete the missing values without having to express the linear function algebraically, which might confuse or hamper the student's understanding of the linear function.