Determine whether the given points are on the graph of \( y=2 x+3 \). Select all points that lie on the graph. (4,6) \( (-4,-6) \) \( (-6,-9) \) \( (-1,1) \)

To determine if the given points lie on the graph of the equation \( y = 2x + 3 \), we can plug in the x-coordinate of each point into the equation and see if the resulting y-value matches the y-coordinate of the point. 1. For the point \( (4,6) \): \[ y = 2(4) + 3 = 8 + 3 = 11 \quad \text{(not on the graph)} \] 2. For the point \( (-4,-6) \): \[ y = 2(-4) + 3 = -8 + 3 = -5 \quad \text{(not on the graph)} \] 3. For the point \( (-6,-9) \): \[ y = 2(-6) + 3 = -12 + 3 = -9 \quad \text{(is on the graph)} \] 4. For the point \( (-1,1) \): \[ y = 2(-1) + 3 = -2 + 3 = 1 \quad \text{(is on the graph)} \] Thus, the points that lie on the graph of \( y=2x+3 \) are: - \( (-6,-9) \) - \( (-1,1) \)