To determine the equation that represents the relationship between the hours ([tex]$x$[/tex]) and the miles driven ([tex]$y$[/tex]), let's first observe the pattern shown in the table.
Given points:
- When [tex]$x = 3$[/tex], [tex]$y = 195$[/tex]
- When [tex]$x = 4$[/tex], [tex]$y = 260$[/tex]
- When [tex]$x = 5$[/tex], [tex]$y = 325$[/tex]
- When [tex]$x = 6$[/tex], [tex]$y = 390$[/tex]
From the question, it is stated that each [tex]$x$[/tex] value is multiplied by 65 to get each [tex]$y$[/tex] value.
Let's verify this relationship with the given points to ensure it holds true:
- For [tex]$x = 3$[/tex]: [tex]$y = 65 \times 3 = 195$[/tex]
- For [tex]$x = 4: $[/tex]y = 65 \times 4 = 260[tex]$
- For $[/tex]x = 5: [tex]$y = 65 \times 5 = 325$[/tex]
- For [tex]$x = 6: $[/tex]y = 65 \times 6 = 390[tex]$
Since the relationship holds true for all given points, the general equation representing this relationship is:
\[ y = 65x \]
Next, we need to determine which point could NOT be on this table. Consider the test point \((2, 100)\):
Let's calculate the $[/tex]y[tex]$ value using our equation for $[/tex]x = 2[tex]$:
\[ y = 65 \times 2 = 130 \]
The test point \((2, 100)\) indicates that the $[/tex]y[tex]$ value should be 100. However, based on our calculated $[/tex]y[tex]$ value, for $[/tex]x = 2[tex]$, we should have $[/tex]y = 130[tex]$. Since the given $[/tex]y[tex]$ value (100) does not match the calculated $[/tex]y$ value (130), the point [tex]\((2, 100)\)[/tex] could NOT be on this table.
In conclusion:
- The equation for this situation is: [tex]\[ y = 65x \][/tex]
- The point [tex]\((2, 100)\)[/tex] could NOT be a point on this table.
