To solve this question, we need to determine if each point in the table satisfies the given pattern, which is that each [tex]\( y \)[/tex] value should be 65 times the corresponding [tex]\( x \)[/tex] value. The equation for this relationship is given by:
[tex]\[ y = 65x \][/tex]
First, let's check each point in the table to ensure they fit this equation.
1. For the point [tex]\((3, 195)\)[/tex]:
- Calculate [tex]\( y \)[/tex] using the equation:
[tex]\[ y = 65 \times 3 = 195 \][/tex]
- Since the calculated [tex]\( y \)[/tex] matches the given [tex]\( y \)[/tex], this point fits the pattern.
2. For the point [tex]\((4, 260)\)[/tex]:
- Calculate [tex]\( y \)[/tex] using the equation:
[tex]\[ y = 65 \times 4 = 260 \][/tex]
- Since the calculated [tex]\( y \)[/tex] matches the given [tex]\( y \)[/tex], this point fits the pattern.
3. For the point [tex]\((5, 325)\)[/tex]:
- Calculate [tex]\( y \)[/tex] using the equation:
[tex]\[ y = 65 \times 5 = 325 \][/tex]
- Since the calculated [tex]\( y \)[/tex] matches the given [tex]\( y \)[/tex], this point fits the pattern.
4. For the point [tex]\((6, 390)\)[/tex]:
- Calculate [tex]\( y \)[/tex] using the equation:
[tex]\[ y = 65 \times 6 = 390 \][/tex]
- Since the calculated [tex]\( y \)[/tex] matches the given [tex]\( y \)[/tex], this point fits the pattern.
Since all the points in the table conform to the equation [tex]\( y = 65x \)[/tex], none of these points deviate from the given pattern. Therefore, there isn't a point among the provided ones that does NOT fit the pattern.
Hence, no point from the provided set of points could NOT be on this table.
