Question

The difference of two integers is 5 a. Translate this verbal rule into an equation where \(x\) represents the larger integer and \(y\) the smaller. b. Use the equation in part a to complete the following table. (TABLE CANNOT COPY) c. Plot the values from the table in part b on an appropriately labeled and scaled coordinate system. (GRAPH CANNOT COPY) d. Connect the points on the graph to obtain graphical representation of the equation in part a.

Short answer

Based on the given step-by-step solution, the short answer question can be: Question: Translate the verbal rule "the difference between the larger integer x and the smaller integer y is 5" into an equation and list 5 possible pairs of integers (x, y) that satisfy this relationship. Answer: The equation is x - y = 5. Possible pairs of integers are: (-2, 3), (-1, 4), (0, 5), (1, 6), and (2, 7).

Step-by-step solution

Translate the verbal rule into an equation

As we're given that the difference between two integers is 5 and \(x\) represents the larger integer while \(y\) represents the smaller integer, we can write this as an equation: $$ x - y = 5 $$

Create the table

Assemble a table with possible values for \(x\) and \(y\). Since there is no condition on the size of the integers, we will assume a range of values for \(y\), and calculate the corresponding \(x\) values using the equation. Here are some example values: | \(y\) | \(x\) | |---|---| | -2 | 3 | | -1 | 4 | | 0 | 5 | | 1 | 6 | | 2 | 7 | These values have been obtained by substituting the value of \(y\) in the equation and solving for \(x\).

Plot the values

We now plot these values on a coordinate system, with \(x\) values on the x-axis and \(y\) values on the y-axis. Mark the corresponding points on the graph as follows: (-2, 3) , (-1, 4), (0, 5), (1, 6), (2, 7)

Connect the points

Connect the points on the graph to represent the equation: $$ x - y = 5 $$ Upon connecting the points, you should observe a straight line with a positive slope. This line represents the relationship between the larger integer \(x\) and the smaller integer \(y\) as described by the given equation.