To determine which set of points lies on the line represented by the equation \( y + 2 = 13(x - 12) \), let's first rewrite the equation in slope-intercept form \( y = mx + b \).
Starting with the original equation:
\[ y + 2 = 13(x - 12) \]
Distributing \( 13 \):
\[ y + 2 = 13x - 156 \]
Subtracting \( 2 \) from both sides:
\[ y = 13x - 158 \]
Now, we need to check each set of points to see if they satisfy this equation.
Set (12, -2) and (15, -1)
- For \( (12, -2) \): \[ y = 13(12) - 158 = 156 - 158 = -2 \quad \text{(True)} \]
- For \( (15, -1) \): \[ y = 13(15) - 158 = 195 - 158 = 37 \quad \text{(False)} \]
Set (−12, 2) and (−11, 3)
- For \( (-12, 2) \): \[ y = 13(-12) - 158 = -156 - 158 = -314 \quad \text{(False)} \]
- For \( (-11, 3) \): \[ y = 13(-11) - 158 = -143 - 158 = -301 \quad \text{(False)} \]
Set (12, -2) and (13, 1)
- For \( (12, -2) \): \[ y = 13(12) - 158 = -2 \quad \text{(True)} \]
- For \( (13, 1) \): \[ y = 13(13) - 158 = 169 - 158 = 11 \quad \text{(False)} \]
Set (−12, 2) and (−9, 3)
- For \( (-12, 2) \): \[ y = 13(-12) - 158 = -314 \quad \text{(False)} \]
- For \( (-9, 3) \): \[ y = 13(-9) - 158 = -117 - 158 = -275 \quad \text{(False)} \]
Based on the calculations, none of the point sets have both points lying on the line.
However, since \( (12, -2) \) is the only point that satisfies the equation from the first set, the answer is:
Set (12, -2) which is present in the first and third options is one point that lies on the line.