To determine the equation that represents the relationship between the number of hours a car drives ([tex]$x$[/tex]) and the number of miles it covers ([tex]$y$[/tex]), we observe the pattern given.
The pattern mentioned is that each [tex]$x$[/tex] value is multiplied by 65 to get the corresponding [tex]$y$[/tex] value. This implies a linear relationship where the coefficient (multiplication factor) is 65. We can represent this relationship as:
[tex]\[ y = 65x \][/tex]
Let's verify this equation with the given data points to ensure it accurately represents the table.
1. For [tex]$x = 3$[/tex]:
[tex]\[ y = 65 \times 3 = 195 \][/tex]
This matches the table entry (3, 195).
2. For [tex]$x = 4$[/tex]:
[tex]\[ y = 65 \times 4 = 260 \][/tex]
This matches the table entry (4, 260).
3. For [tex]$x = 5$[/tex]:
[tex]\[ y = 65 \times 5 = 325 \][/tex]
This matches the table entry (5, 325).
4. For [tex]$x = 6$[/tex]:
[tex]\[ y = 65 \times 6 = 390 \][/tex]
This matches the table entry (6, 390).
Since the equation [tex]\( y = 65x \)[/tex] holds true for all the provided data points, this is the correct representation of the relationship between hours and miles in the given scenario.
To answer the given questions:
1. The equation for this situation is:
[tex]\[ y = 65x \][/tex]
2. The point [tex]$(4, 260)$[/tex] is part of the table and corresponds to [tex]$x = 4$[/tex] and [tex]$y = 260$[/tex]. It fits the pattern and equation perfectly.
