Question

Which rule describes the relationship between the x- and y-coordinates in the following table?

Answer 1

Answer:

y = x + 5

Explanations:

There is a constant rate of change in the table, therefore, the slope can be calculated by considering any two rows on the table

Considering the points (10, 15) and (13, 18)

`\begin{gathered} m\text{ = }(y_2-y_1)/(x_2-x_1) \\ m\text{ = }(18-15)/(13-10) \\ m\text{ = }(3)/(3) \\ m\text{ = 1} \end{gathered}`

Using the equation:

`\begin{gathered} y-y_1=m(x-x_1) \\ x_1=10,y_1=\text{ 15} \\ y\text{ - 15 = 1(x - 10)} \\ y\text{ - 15 = x - 10} \\ y\text{ = x - 10 + 15} \\ y\text{ = x + 5} \end{gathered}`

The rule that describes the relationship between x and y is y = x + 5