What is the equation for this situation? Which could NOT be a point on this table?

Steps to Solve

1. Identifying the Relationship Between Variables
   The table shows a pattern where each hour driven (x) corresponds to a specific number of miles driven (y). The relationship given is that for each hour, the miles are calculated by multiplying the hours by 65.

2. Formulating the Equation
   To form the equation based on the relationship identified, we can express it as:
   $$ y = 65x $$
   This means for every hour driven (x), the miles driven (y) is calculated by multiplying the number of hours by 65.

3. Verifying the Points in the Table
   Check each entry in the table using the equation ( y = 65x ):

   • For ( x = 3 ):
     $$ y = 65 \times 3 = 195 $$
   • For ( x = 4 ):
     $$ y = 65 \times 4 = 260 $$
   • For ( x = 5 ):
     $$ y = 65 \times 5 = 325 $$
   • For ( x = 6 ):
     $$ y = 65 \times 6 = 390 $$

   All points in the table match the equation.

4. Finding Points Not in the Table
   To identify a point that could NOT be represented in the table, we need to determine values of ( x ) that don't yield integer results for ( y ) or don't fit the pattern. For example, if ( x = 7 ):
   $$ y = 65 \times 7 = 455 $$
   If this point (7, 455) was not included, then it could NOT be a point in the table.