Question

The following table shows a proportional relationship between m and n. m 3 21 5 35 8 56 Write an equation to describe the relationship between m and n.

Answer 1

In order to write an equation for m and n, let's use the slope-intercept form of the linear equation:

`n=am+b`

Where a is the slope and b is the y-intercept.

To find the values of a and b, let's use two points of the table:

`\begin{gathered} (3,21)\colon \\ 21=3a+b \\ (5,35)\colon \\ 35=5a+b \end{gathered}`

Subtracting the second and first equation, we have:

`\begin{gathered} 35-21=5a+b-(3a+b) \\ 14=2a \\ a=7 \\ \\ 21=3a+b \\ 21=21+b \\ b=0 \end{gathered}`

So our equation is:

`n=7m`