NC.M1.F-IF.2, NC.M1.F-IF.5) Mastering the Standard Comprehending the Standard Assessing for Understanding Students understand that the graph of an Students should be able to assess if a point is a solution to an equation. equation is the set of all ordered pairs that make Example: Consider three points in the plane, that equation a true statement. Find the equation of the line through and . Use your equation in (a) to show that is on the same line as and . This standard contains no limitation and so () applies to all function types, including those functions that a student cannot yet algebraically Example: of the following points are on the graph of the equation Which of the following points are of the manipulate. graph of the equation? How do you know? (4, 0) Students can explain and verify that every point (0, 10) (x, on the graph of an equation represents all (-1, 7.5) y) values for and that make the equation true. (2.3, 5) x y Example: Verify that is a solution to the equation . Explain what this means for the graph of the function. Example: Without graphing, determine if the ordered pair is on the graph of . Explain. Example: The graph below shows the height of a hot air balloon as a function of time. Use the graph to answer the following: What is the height of the hot air balloon 10 minutes after it has left the ground? Approximately, when will the hot air balloon reach a height of 600 feet? Explain what the on this graph represents. Instructional Resources Tasks Additional Resources (Illustrative Mathematics) Back to: Algebra Reasoning with Equations and Inequalities – NC.M1.A-REI.11 Represent and solve equations and inequalities graphically Build an understanding of why the of the points where the graphs of two linear, exponential, or quadratic equations and intersect x-coordinates are the solutions of the equation and approximate solutions using a graphing technology or successive approximations with a table of values. Concepts and Skills The Standards for Mathematical Practices
NC.M1.F-IF.2, NC.M1.F-IF.5) Mastering the Standard Comprehending the Standard Assessing for Understanding Students understand that the graph of an equation is the set of all ordered pairs that make that equation a true statement. This standard contains no limitation and so applies to all function types, including those functions that a student cannot yet algebraically manipulate. Students can explain and verify that every point (x, y) on the graph of an equation represents all values for x and y that make the equation true. Students should be able to assess if a point is a solution to an equation. Example: Consider three points in the plane, Find the equation of the line through and . Use your equation in (a) to show that is on the same line as and . () Example: of the following points are on the graph of the equation Which of the following points are of the graph of the equation? How do you know? (4, 0) (0, 10) (-1, 7.5) (2.3, 5) Example: Verify that is a solution to the equation . Explain what this means for the graph of the function. Example: Without graphing, determine if the ordered pair is on the graph of . Explain. Example: The graph below shows the height of a hot air balloon as a function of time. Use the graph to answer the following: What is the height of the hot air balloon 10 minutes after it has left the ground? Approximately, when will the hot air balloon reach a height of 600 feet? Explain what the on this graph represents. Instructional Resources Tasks Additional Resources (Illustrative Mathematics) Back to: Algebra – Reasoning with Equations and Inequalities NC.M1.A-REI.11 Represent and solve equations and inequalities graphically Build an understanding of why the x-coordinates of the points where the graphs of two linear, exponential, or quadratic equations and intersect are the solutions of the equation and approximate solutions using a graphing technology or successive approximations with a table of values. Concepts and Skills The Standards for Mathematical Practices
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