Connection Among Equation, Graph and Table of Values

The sliders allow you to change the values of 'm' and 'b' in the equation y = mx + b. By moving the sliders, you can see how the values in the table of values change. You can also see how the points on the graph and the line on the graph change. Your goal is to be able to how the three descriptions (equation, graph and table of values) for a linear relation are connected.
Task #1: The role of 'b' Slowly change the value of 'b' using the slider. (a) What effect does increasing the value of 'b' have on the position of the line on the graph? What happens when the value of 'b' decreases? (b) What happens to the y-values in the table when the value of 'b' is increased by 1? What if 'b' is decreased by 1? (c) Compare the initial value for the relation (the y-value in the table when the x-value is 0), the y-intercept on the graph (the number on the y-axis where the line crosses), and the value of 'b'? What do you notice? Task #2: The role of 'm' Slowly change the value of 'm' using the slider. (a) What effect does increasing the value of 'm' (moving the slider to the right) have on the steepness of the line when 'm' is a positive number? (b) What effect does decreasing the value of 'm' (moving the slider to the left) have on the steepness of the line when 'm' is a negative number? (c) Describe the steepness of the line when m = 0. Set the value of 'm' on the slider to 2. (d) Calculate the slope of the line. Remember that (e) Calculate the first differences of the table. (f) Compare your answers to (d) and (e) to each other, to the value of 'm', and to the number that multiplies the 'x' in the equation. Make a conclusion.