To determine which set of points lies on the line represented by the equation \( y + 2 = \frac{1}{3}(x - 12) \), we first need to rearrange this equation into the slope-intercept form \( y = mx + b \).
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Rearranging the equation:
Start with \( y + 2 = \frac{1}{3}(x - 12) \).
Distributing the \( \frac{1}{3} \): \[ y + 2 = \frac{1}{3}x - 4 \]
Subtracting 2 from both sides: \[ y = \frac{1}{3}x - 4 - 2 \] \[ y = \frac{1}{3}x - 6 \]
Now the equation of the line in slope-intercept form is \( y = \frac{1}{3}x - 6 \).
- Testing the points:
To determine whether specific points lie on the line, you can plug in the x-values from each point into the equation \( y = \frac{1}{3}x - 6 \) and check if the resulting y-value matches the y-value of the point.
If you provide the set of points you want to test, I'll help you check each one!