To determine which of the given points lies on the line described by the equation \( y - 5 = 6(x - 7) \), we can rearrange the equation into slope-intercept form (y = mx + b) and then see if the points satisfy the equation.
Starting with: \[ y - 5 = 6(x - 7) \]
We can expand and simplify: \[ y - 5 = 6x - 42 \] \[ y = 6x - 42 + 5 \] \[ y = 6x - 37 \]
Now, we can test each of the given points to see if they satisfy the equation \( y = 6x - 37 \).
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Point (7, 5): \[ y = 6(7) - 37 = 42 - 37 = 5 \quad \text{(satisfies the equation)} \]
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Point (-7, -5): \[ y = 6(-7) - 37 = -42 - 37 = -79 \quad \text{(does not satisfy the equation)} \]
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Point (-5, -7): \[ y = 6(-5) - 37 = -30 - 37 = -67 \quad \text{(does not satisfy the equation)} \]
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Point (5, 7): \[ y = 6(5) - 37 = 30 - 37 = -7 \quad \text{(does not satisfy the equation)} \]
The only point that lies on the line is:
(7, 5).