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.

In order to write an equation for m and n, let's use the slope-intercept form of the linear equation:
[tex]n=am+b[/tex]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:
[tex]\begin{gathered} (3,21)\colon \\ 21=3a+b \\ (5,35)\colon \\ 35=5a+b \end{gathered}[/tex]Subtracting the second and first equation, we have:
[tex]\begin{gathered} 35-21=5a+b-(3a+b) \\ 14=2a \\ a=7 \\ \\ 21=3a+b \\ 21=21+b \\ b=0 \end{gathered}[/tex]So our equation is:
[tex]n=7m[/tex]