Overview
Prior Knowledge
The following Michigan Grade Level Content Expectations will be needed to understand this unit:
A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.
A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.
A.PA.07.03 Given a directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit.
A.PA.07.04 For directly proportional or other linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed.
A.PA.07.05 Recognize and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.
A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of "rise/run" for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change.
A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.
A.FO.07.08 Find and interpret the x and/or y intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax + b = 0 corresponds to the point at which the graph of y = ax + b crosses the x axis.
A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) - 5x + y, or x(x+2), and justify using properties of real numbers.
A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx +d, and interpret solutions.
A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).
A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.
A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.
A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities.
A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.
A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations.
A.PA.07.03 Given a directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = mx + b for specific x values, e.g., weight vs. volume of water, base cost plus cost per unit.
A.PA.07.04 For directly proportional or other linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section; height of water in a tank being filled at a constant rate; degrees Celsius and degrees Fahrenheit; distance and time under constant speed.
A.PA.07.05 Recognize and use directly proportional relationships of the form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity.
A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of "rise/run" for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change.
A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept.
A.FO.07.08 Find and interpret the x and/or y intercepts of a linear equation or function. Know that the solution to a linear equation of the form ax + b = 0 corresponds to the point at which the graph of y = ax + b crosses the x axis.
A.FO.07.12 Add, subtract, and multiply simple algebraic expressions of the first degree, e.g., (92x + 8y) - 5x + y, or x(x+2), and justify using properties of real numbers.
A.FO.07.13 From applied situations, generate and solve linear equations of the form ax + b = c and ax + b = cx +d, and interpret solutions.
A.FO.08.10 Understand that to solve the equation f(x) = g(x) means to find all values of x for which the equation is true, e.g., determine whether a given value, or values from a given set, is a solution of an equation (0 is a solution of 3x2 + 2 = 4x + 2, but 1 is not a solution).
A.FO.08.11 Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions.
A.FO.08.12 Solve linear inequalities in one and two variables, and graph the solution sets.
A.FO.08.13 Set up and solve applied problems involving simultaneous linear equations and linear inequalities.