Relating the 4 Ways to Describe a Linear Relation

By moving sliders in the activity, you will learn how the four ways you learned to describe linear relations - equation, graph, table of values and word description - relate to each other. This will help you to convert one way to describe a linear relation into any of the other ways.
Task #1. The Effect of 'b' Use the slider for 'b' to change the value of 'b' and observe how the graph, table, equation and sentence are changed. (a) Describe what happens to the graph as the value of 'b' is (i) increased and (ii) decreased. Compare the location where the graph crosses the vertical (up and down) axis with the value of 'b'. Does the value of 'b' affect the steepness of the graph? (b) Compare the numbers in the equation to the value of 'b'. What do you notice? (c) Compare the initial value for the table (the value of y when the value of x is 0) to the value of 'b'. What do you notice? Does the value of 'b' affect the values of the first differences? (d) What changes in the sentence description as the value of 'b' is changed? Task #2 The Effect of 'm' Use the slider for 'm' to change the value of 'm' and observe how the graph, table, equation and sentence are changed. (a) Describe what happens to the graph as the value of 'm' is (i) increased and (ii) decreased when the value of 'm' is positive. What happens to the graph as the value of 'm' is (i) increased (the slider goes to the right) and (ii) decreased (the slider goes to the left) when the value of 'm' is negative. Does the value of 'm' affect the place where the graph crosses the vertical axis? (b) Compare the numbers in the equation to the value of 'm'. What do you notice? (c) Compare the values of the first differences to the value of 'm'. What do you notice? Does the value of 'm' affect the initial value? (d) What changes in the sentence description as the value of 'm' is changed?