Question

={8a4c2d72-6d4...MAShare- The table compares the ages, in years, of twocousins.4812Ann's age,Tom's age, y81216a. Write an equation that compares Tomsand Ann's ages.Y=2xb. Draw a graph to represent theequation.8642.O2.461:39 PM3/10/2021

Answer 1

We have a table of values that shows the ages of two individuals. The data can be written out as an ordered pair as follows;

`\begin{gathered} (4,8),(8,12),(12,16) \\ \text{Where Ann's age is x and Tom's age is y} \\ \text{The slope m is derived below;} \\ m=(y_2-y_1)/(x_2-x_1) \\ m=(12-8)/(8-4) \\ m=(4)/(4) \\ m=1 \\ We\text{ can now insert the known values, x, y and m} \\ y=mx+b \\ \text{This becomes;} \\ 8=1(4)+b \\ 8=4+b \\ 8-4=b \\ b=4 \\ \text{The equation } \\ y=mx+b \\ Is\text{ now expressed as,} \\ y=(1)x+4 \\ y=x+4 \end{gathered}`

The equation is now represented on a graph as shown;