10. Select all the points that are on a line with slope 2 . that also contains the point \( (2,-1) \). (A.) \( (3,1) \) (B. \( (1,1) \) (C. \( (1,-3) \) (D. \( (4,0) \) (E. \( (6,7) \)

To determine which points are on the line with a slope of 2 that passes through the point \( (2,-1) \), we can use the point-slope form of the equation of a line: \[ y - y_1 = m(x - x_1) \] Plugging in the point \( (2,-1) \) and the slope \( 2 \): \[ y - (-1) = 2(x - 2) \] Simplifying this gives us: \[ y + 1 = 2x - 4 \] \[ y = 2x - 5 \] Now we can test each point to see if it satisfies this equation. (A.) For \( (3,1) \): \[ y = 2(3) - 5 = 6 - 5 = 1 \] ✔️ (B.) For \( (1,1) \): \[ y = 2(1) - 5 = 2 - 5 = -3 \] ❌ (C.) For \( (1,-3) \): \[ y = 2(1) - 5 = 2 - 5 = -3 \] ✔️ (D.) For \( (4,0) \): \[ y = 2(4) - 5 = 8 - 5 = 3 \] ❌ (E.) For \( (6,7) \): \[ y = 2(6) - 5 = 12 - 5 = 7 \] ✔️ The points on the line are \( (3,1) \), \( (1,-3) \), and \( (6,7) \).