what is the equation

1. Note the equation \(\frac{Y_2-Y_1}{X_2-X_1}\)

 

2. Substitute \(\frac{(30)-(16)}{(5)-(2)}\)

 

3. Solve \(\frac{14}{3}\)

 

4.  Note the equation \(y=mx+b\)

 

We already have \(m\), which is \(\frac{14}{3}\)

 

So \(y=\frac{14}{3}x+b\)

 

5. Substitute a coordinate \((x,y)\), from the problem

 

Take \((2,16)\) and substitute it in to get: \(16=\frac{14}{3}*(2)+b\)

 

Solving we get \(b=\frac{20}{3}\)

 

6. Put \(b\) and \(m\) together to make the equation \(\boxed{y=\frac{14}{3}x+\frac{20}{3}}\)