Students calculate the rate of change also know as the constant of proportionality (k = y/x) which is the constant ratio between two proportional quantities y/x denoted by the symbol k which may be a positive rational number. The x value is directly proportional to the y value such as in the equation y = kx. Students should also understand that d = rt is a proportional relationship and a specific example of y = kx.The constant of proportionality includes, a graphed proportional relationship where x represents the independent variable and y represents the dependent variable, independent variables describe the input values in a relationship, normally represented by the x coordinate in the ordered pairs (x, y), and dependent variables describe the output values in a relationship, normally represented by the y coordinate in the ordered pairs (x, y). The constant of proportionality can never be zero.Students must also be familiar with the various representations of the constant of proportionality such as in a vertical or horizontal table, with numeric, a verbal description, in a graph, or algebraically.
Jimmy runs 126 miles in 3 days in his school running club. What is the constant of proportionality that relates the number of miles, y, to the number of days, x?
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(4) Proportionality. The student applies mathematical process standards to represent and solve problems involving proportional relationships. The student is expected to:
(C) determine the constant of proportionality (k = y/x) within mathematical and real-world problems