Find the Change

The table below shows two coordinate pairs $(x, y)$ that satisfy the equation $y=mx+b$ for some numbers $m$ and $b$.
$x$ $y$ 2 $y_1$ 5 $y_2$ 
If $m = 7$, determine possible values for $y_1$ and $y_2$. Explain your choices.
Find another pair of $y$values that could work for $m = 7$. Explain why they would work. How do these $y$values compare to the first pair you found for $m = 7$?
Use the same $x$values in the table and find possible values for $y_1$ and $y_2$ if $m=3$. Explain your choices.
Find another pair of $y$values that could work for $m = 3$. Explain why they would work. How do these $y$values compare to the first pair you found for $m = 3$?


Each of the three tables below shows two coordinate pairs $(x, y)$ that satisfy the equation $y=mx+b$ for some numbers $m$ and $b$. If $m = 3$ in each case, find possible values for $y_1$ and $y_2$ for each pair of $x$values given.

$x$ $y$ 4 $y_1$ 9 $y_2$ 
$x$ $y$ 2 $y_1$ 13 $y_2$ 
$x$ $y$ 1 $y_1$ 14 $y_2$ 
Suppose we take all six $x$values from the three tables above. Can you find six corresponding $y$values so that all the coordinate pairs satisfy the same equation if $m=3$? Fill out the table below and explain how you know they will all work with the same equation.
$x$ $y$ 4 9 2 13 1 14
